Economics - Demand, Supply, and Markets

Demand

Definition

Demand is the willingness and ability of consumers to purchase goods and services at various prices during a given period of time, ceteris paribus (all other things being equal).

The Law of Demand

As the price of a good increases, the quantity demanded decreases, and vice versa. This gives a downward-sloping demand curve.

Exceptions to the Law of Demand

• Giffen goods: Inferior goods where the income effect outweighs the substitution effect. As price rises, quantity demanded rises.
• Veblen goods: Luxury goods where higher price increases perceived status and desirability.
• Speculative demand: When consumers expect future price increases, they may buy more at current high prices.

Demand Schedule and Demand Curve

Price (USD)	Quantity Demanded
10	100
20	80
40	50
60	30
80	10

Movements Along vs Shifts of the Demand Curve

Movement along the curve: Caused by a change in the price of the good itself (change in quantity demanded).

Shift of the curve: Caused by a change in non-price factors (change in demand).

Factors Shifting Demand

Factor	Effect on Demand
Increase in income (normal good)	Demand shifts right
Increase in income (inferior good)	Demand shifts left
Increase in price of substitute	Demand shifts right
Increase in price of complement	Demand shifts left
Change in tastes towards the good	Demand shifts right
Increase in population	Demand shifts right
Expectation of future price increase	Demand shifts right
Successful advertising	Demand shifts right

tip

Remember: a change in the good's own price causes movement along the curve. A change in any other factor causes a shift of the curve. DSE exams frequently test this distinction.

Individual Demand vs Market Demand

Market demand is the horizontal sum of all individual demands at each price level.

$Q_D = q_1 + q_2 + q_3 + \ldots + q_n$

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Supply

Definition

Supply is the willingness and ability of producers to offer goods and services for sale at various prices during a given period of time, ceteris paribus.

The Law of Supply

As the price of a good increases, the quantity supplied increases, and vice versa. This gives an upward-sloping supply curve.

The law of supply is based on the profit motive: higher prices make production more profitable, incentivising producers to supply more.

Movements Along vs Shifts of the Supply Curve

Movement along the curve: Caused by a change in the price of the good itself (change in quantity supplied).

Shift of the curve: Caused by a change in non-price factors (change in supply).

Factors Shifting Supply

Factor	Effect on Supply
Decrease in production costs	Supply shifts right
Improvement in technology	Supply shifts right
Increase in number of suppliers	Supply shifts right
Government subsidy	Supply shifts right
Government tax	Supply shifts left
Increase in price of factors of production	Supply shifts left
Adverse weather (agricultural goods)	Supply shifts left
Expectation of future price increase	Supply shifts left (withhold stock)

warning

warning "increase in supply" (shift). Be precise with terminology.

Market Supply

Market supply is the horizontal sum of all individual firm supplies:

$Q_S = q_1 + q_2 + q_3 + \ldots + q_n$

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Market Equilibrium

Definition

Market equilibrium occurs where quantity demanded equals quantity supplied ($Q_D = Q_S$). At this point, the market clears and there is no tendency for the price to change.

The equilibrium price is also called the market-clearing price.

Worked Example 1

Given $Q_D = 100 - 2P$ and $Q_S = 20 + 3P$, find the equilibrium price and quantity.

At equilibrium: $Q_D = Q_S$

$100 - 2P = 20 + 3P$

$80 = 5P$

$P = 16$

$Q = 100 - 2(16) = 100 - 32 = 68$

Disequilibrium

Surplus (excess supply): When $P \gt P_e$, $Q_S \gt Q_D$. Price tends to fall.

Shortage (excess demand): When $P \lt P_e$, $Q_D \gt Q_S$. Price tends to rise.

Changes in Equilibrium

Change	Effect on $P_e$	Effect on $Q_e$
Demand increases, supply constant	Rises	Rises
Demand decreases, supply constant	Falls	Falls
Supply increases, demand constant	Falls	Rises
Supply decreases, demand constant	Rises	Falls
Both demand and supply increase	Ambiguous	Rises
Both demand and supply decrease	Ambiguous	Falls

Worked Example 2

If demand increases by 30 units at every price (new $Q_D = 130 - 2P$), find the new equilibrium.

$130 - 2P = 20 + 3P$

$110 = 5P$

$P = 22$

$Q = 130 - 2(22) = 86$

Price rose from 16 to 22; quantity rose from 68 to 86.

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Price Elasticity of Demand (PED)

Definition

PED measures the responsiveness of quantity demanded to a change in price:

$\mathrm{PED} = \frac{\%\ \mathrm{change in quantity demanded}}{\%\ \mathrm{change in price}} = \frac{\Delta Q / Q}{\Delta P / P}$

Since demand curves slope downward, PED is usually negative. By convention, we often report the absolute value.

Categories of PED

Value	Description	Meaning
PED = 0	Perfectly inelastic	Quantity demanded does not change at all
0 < PED < 1	Inelastic	Quantity changes proportionally less than price
PED = 1	Unit elastic	Quantity changes proportionally equal to price
PED > 1	Elastic	Quantity changes proportionally more than price
PED = infinity	Perfectly elastic	Any price increase reduces quantity demanded to zero

Factors Affecting PED

Factor	Higher PED	Lower PED
Availability of substitutes	Many substitutes	Few substitutes
Proportion of income spent	Large proportion	Small proportion
Necessity vs luxury	Luxury goods	Necessities
Time period	Long run (more time to adjust)	Short run
Definition of market	Narrow market (specific good)	Broad market (category)

PED and Total Revenue

$\mathrm{Total Revenue (TR)} = P \times Q$

PED	Price Increase	Price Decrease
Elastic (PED > 1)	TR decreases	TR increases
Inelastic (PED < 1)	TR increases	TR decreases
Unit elastic (PED = 1)	TR unchanged	TR unchanged

tip

If a firm wants to increase revenue, it should lower price if demand is elastic and raise price if demand is inelastic. This is a very common exam question.

Worked Example 3

The price of a good increases from USD 50 to USD 60. Quantity demanded falls from 200 to 160 units. Calculate PED.

$\%\ \mathrm{change in } Q = \frac{160 - 200}{200} \times 100\% = -20\%$

$\%\ \mathrm{change in } P = \frac{60 - 50}{50} \times 100\% = 20\%$

$\mathrm{PED} = \frac{-20\%}{20\%} = -1$

PED = 1 (unit elastic by initial-value method). Note: total revenue changes from $50 \times 200 = 10\,000$ to $60 \times 160 = 9\,600$ (a decrease of 400). The rule "PED = 1 implies TR unchanged" is exact only for point elasticity on a demand curve of the form $P = k/Q$; for a linear demand curve with finite changes, the initial-value PED of $-1$ does not guarantee constant TR.

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Price Elasticity of Supply (PES)

Definition

PES measures the responsiveness of quantity supplied to a change in price:

$\mathrm{PES} = \frac{\%\ \mathrm{change in quantity supplied}}{\%\ \mathrm{change in price}} = \frac{\Delta Q / Q}{\Delta P / P}$

PES is usually positive because supply curves slope upward.

Categories of PES

Value	Description
PES = 0	Perfectly inelastic (vertical supply curve)
0 < PES < 1	Inelastic
PES = 1	Unit elastic
PES > 1	Elastic
PES = infinity	Perfectly elastic (horizontal supply curve)

Factors Affecting PES

Factor	Higher PES	Lower PES
Time period	Long run (firms can adjust)	Short run (fixed factors)
Mobility of factors	Highly mobile	Immobile
Spare capacity	Lots of spare capacity	Operating at full capacity
Storage ability	Easy to store	Perishable goods
Complexity of production	Simple production	Complex production

Worked Example 4

Price rises from USD 40 to USD 50. Quantity supplied rises from 300 to 450 units. Calculate PES.

$\%\ \mathrm{change in } Q = \frac{450 - 300}{300} \times 100\% = 50\%$

$\%\ \mathrm{change in } P = \frac{50 - 40}{40} \times 100\% = 25\%$

$\mathrm{PES} = \frac{50\%}{25\%} = 2$

Supply is elastic (PES = 2 > 1).

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Income Elasticity of Demand (YED)

Definition

YED measures the responsiveness of quantity demanded to a change in income:

$\mathrm{YED} = \frac{\%\ \mathrm{change in quantity demanded}}{\%\ \mathrm{change in income}}$

Categories

YED Value	Type of Good	Example
YED < 0	Inferior good	Generic brands, public transport
0 < YED < 1	Normal good (necessity)	Rice, basic clothing
YED > 1	Normal good (luxury)	Designer clothing, fine dining

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Cross Elasticity of Demand (XED)

Definition

XED measures the responsiveness of quantity demanded of one good to a change in the price of another good:

$\mathrm{XED} = \frac{\%\ \mathrm{change in quantity demanded of good A}}{\%\ \mathrm{change in price of good B}}$

Categories

XED Value	Relationship	Example
XED > 0	Substitutes	Tea and coffee
XED < 0	Complements	Cars and petrol
XED = 0	Unrelated goods	Cars and bread

The larger the absolute value of XED, the stronger the relationship between the goods.

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Government Intervention

Price Controls

Price Ceiling (Maximum Price): Set below equilibrium price to make goods more affordable.

• Creates a shortage (excess demand)
• May lead to black markets, rationing, reduced quality
• Example: rent control

Price Floor (Minimum Price): Set above equilibrium price to protect producers.

• Creates a surplus (excess supply)
• May require government purchasing of surplus
• Example: minimum wage, agricultural price supports

Worked Example 5

Given $Q_D = 200 - 4P$ and $Q_S = 40 + 2P$, the government sets a price ceiling at USD 20. Find the resulting shortage.

At $P = 20$:

$Q_D = 200 - 4(20) = 200 - 80 = 120$

$Q_S = 40 + 2(20) = 40 + 40 = 80$

Shortage $= Q_D - Q_S = 120 - 80 = 40$ units

Taxes

A tax shifts the supply curve upward (leftward) by the amount of the tax.

Specific tax (per unit): A fixed amount per unit sold.

Ad valorem tax: A percentage of the price.

Tax Incidence (Burden)

The burden of a tax is shared between consumers and producers. The distribution depends on elasticity:

• If demand is inelastic relative to supply: consumers bear most of the tax burden
• If supply is inelastic relative to demand: producers bear most of the tax burden

$\mathrm{Consumer burden} = P_{\mathrm{after tax}} - P_{\mathrm{before tax}}$

$\mathrm{Producer burden} = P_{\mathrm{before tax}} - P_{\mathrm{after tax (net)}}$

Worked Example 6

Given $Q_D = 100 - P$ and $Q_S = P - 20$, a specific tax of USD 10 per unit is imposed. Find the new equilibrium, tax revenue, and the burden on consumers and producers.

Original equilibrium: $100 - P = P - 20$, so $2P = 120$, $P = 60$, $Q = 40$.

With tax, the supply becomes $Q_S = (P - 10) - 20 = P - 30$ (producers receive $P - 10$):

$100 - P = P - 30$

$130 = 2P$

$P = 65$ (price consumers pay)

$Q = 100 - 65 = 35$

Producers receive $65 - 10 = 55$.

Tax revenue $= 10 \times 35 = 350$

Consumer burden $= 65 - 60 = 5$ per unit

Producer burden $= 60 - 55 = 5$ per unit

Subsidies

A subsidy shifts the supply curve downward (rightward). Consumers pay less and producers receive more.

$\mathrm{Consumer benefit} = P_{\mathrm{before}} - P_{\mathrm{after}}$

$\mathrm{Producer benefit} = (P_{\mathrm{after}} + \mathrm{subsidy}) - P_{\mathrm{before}}$

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Market Failure

Definition

Market failure occurs when the free market fails to allocate resources efficiently, resulting in a loss of economic welfare (deadweight loss).

Types of Market Failure

1. Externalities

An externality is a cost or benefit that affects a third party who did not choose to incur that cost or benefit.

Negative externality (external cost): The social cost exceeds the private cost.

$\mathrm{MSC} = \mathrm{MPC} + \mathrm{MEC}$

Where MSC = marginal social cost, MPC = marginal private cost, MEC = marginal external cost.

Example: pollution from a factory affects the health of nearby residents.

Positive externality (external benefit): The social benefit exceeds the private benefit.

$\mathrm{MSB} = \mathrm{MPB} + \mathrm{MEB}$

Where MSB = marginal social benefit, MPB = marginal private benefit, MEB = marginal external benefit.

Example: vaccination benefits not only the vaccinated person but also the community.

2. Public Goods

Public goods are non-excludable and non-rivalrous.

Characteristic	Public Goods	Private Goods
Excludability	Non-excludable	Excludable
Rivalry	Non-rivalrous	Rivalrous
Example	National defence, street lighting	Food, clothing

The free-rider problem means private firms will not produce public goods because they cannot charge beneficiaries. Government must provide them.

3. Information Asymmetry

When one party has more information than the other, market outcomes may be inefficient.

• Adverse selection: Occurs before a transaction (e.g., selling a used car with hidden defects)
• Moral hazard: Occurs after a transaction (e.g., taking more risks after buying insurance)

4. Monopoly Power

A monopoly can restrict output and raise prices above the competitive level, causing deadweight loss.

Government Solutions to Market Failure

Market Failure	Policy
Negative externality	Tax (Pigouvian tax), regulation, tradable permits
Positive externality	Subsidy, direct provision, regulation
Public goods	Direct government provision
Information asymmetry	Regulation, certification, labelling requirements
Monopoly power	Anti-trust laws, price regulation, privatisation

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Summary Table

Topic	Key Concept	Formula
Law of Demand	Price up, quantity down	Downward-sloping curve
Law of Supply	Price up, quantity up	Upward-sloping curve
Equilibrium	$Q_D = Q_S$	Market clears
PED	Responsiveness of demand to price	$\frac{\%\Delta Q_D}{\%\Delta P}$
PES	Responsiveness of supply to price	$\frac{\%\Delta Q_S}{\%\Delta P}$
YED	Responsiveness of demand to income	$\frac{\%\Delta Q_D}{\%\Delta Y}$
XED	Relationship between goods	$\frac{\%\Delta Q_{DA}}{\%\Delta P_B}$
Tax incidence	Depends on elasticity	More inelastic side pays more

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Exam Tips

• Always distinguish between a "change in demand/supply" (shift) and a "change in quantity demanded/supplied" (movement along).
• When drawing diagrams, label all axes, curves, and equilibrium points clearly.
• For PED questions, remember that TR is maximised when PED = 1.
• When analysing taxes and subsidies, clearly identify who pays and who receives, and calculate the burden on each side.
• For market failure questions, always identify the type of externality and explain why the free market over- or under-produces.
• Use the concept of deadweight loss to explain the welfare impact of market failure.

Exam-Style Practice Questions

Question 1: The demand function is $Q_D = 300 - 5P$ and the supply function is $Q_S = 2P - 60$. Find the equilibrium price and quantity.

$300 - 5P = 2P - 60$

$360 = 7P$

$P = 51.43$, $Q = 300 - 5(51.43) = 42.86$

Question 2: A 20% increase in the price of good A causes a 10% decrease in the quantity demanded of good B. What is the relationship between the goods?

$\mathrm{XED} = \frac{-10\%}{20\%} = -0.5$

Since XED is negative, goods A and B are complements.

Question 3: Explain why the government may impose a price ceiling on rent. What problems might arise?

A price ceiling makes housing more affordable for low-income households. However, it creates a shortage (excess demand), may reduce the quality and maintenance of rental properties, and could lead to black market activities. Landlords may convert properties to other uses, reducing long-run supply.

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Production, Costs, and Revenue

Production in the Short Run and Long Run

Short run: At least one factor of production is fixed (e.g., factory size). Firms can only vary output by changing variable factors (e.g., labour, raw materials).

Long run: All factors of production are variable. Firms can change their scale of production.

Law of Diminishing Marginal Returns

As more of a variable factor is added to a fixed factor, the marginal product of the variable factor will eventually decrease.

Units of Labour	Total Product	Marginal Product	Average Product
0	0	—	—
1	10	10	10.0
2	25	15	12.5
3	45	20	15.0
4	60	15	15.0
5	70	10	14.0
6	75	5	12.5
7	75	0	10.7
8	70	-5	8.75

Marginal product starts to diminish after the 3rd worker. Negative marginal product begins at the 8th worker (overcrowding).

Costs of Production

Cost	Definition	Formula
Total fixed cost (TFC)	Cost of fixed factors; does not change with output	—
Total variable cost (TVC)	Cost of variable factors; changes with output	—
Total cost (TC)	Sum of all costs	TC = TFC + TVC
Average fixed cost (AFC)	Fixed cost per unit	AFC = TFC / Q
Average variable cost (AVC)	Variable cost per unit	AVC = TVC / Q
Average total cost (ATC)	Total cost per unit	ATC = TC / Q
Marginal cost (MC)	Cost of producing one more unit	MC = change in TC / change in Q

Cost Curves

• AFC is always downward sloping (fixed cost spread over more units)
• AVC is U-shaped (initially falls due to increasing returns, then rises due to diminishing returns)
• ATC is U-shaped (sum of AFC and AVC)
• MC is U-shaped; it intersects AVC and ATC at their minimum points
• MC passes below ATC when ATC is falling, and above ATC when ATC is rising

info

info because when MC \lt ATC, it pulls ATC down; when MC \gt ATC, it pulls ATC up.

Revenue

Revenue	Definition	Formula
Total revenue (TR)	Total income from sales	TR = P $\times$ Q
Average revenue (AR)	Revenue per unit	AR = TR / Q = P
Marginal revenue (MR)	Revenue from selling one more unit	MR = change in TR / change in Q

Profit Maximisation

A firm maximises profit where marginal revenue equals marginal cost (MR = MC).

• If MR \gt MC: producing more increases profit
• If MR \lt MC: producing less increases profit
• If MR = MC: profit is maximised

Worked Example 7

Given the following data, find the profit-maximising output.

Output (Q)	Price (USD)	TC (USD)
0	50	30
1	50	60
2	50	80
3	50	105
4	50	140
5	50	185
6	50	240

Q	TR (USD)	MR (USD)	MC (USD)
0	0	—	—
1	50	50	30
2	100	50	20
3	150	50	25
4	200	50	35
5	250	50	45
6	300	50	55

MR = MC between Q = 5 (MR = 50, MC = 45) and Q = 6 (MR = 50, MC = 55). Profit is maximised at Q = 5 where MR is closest to MC.

Maximum profit: TR - TC = 250 - 185 = USD 65.

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Market Structures

Perfect Competition

Characteristics:

• Many buyers and sellers
• Homogeneous (identical) products
• Perfect information
• Free entry and exit
• Firms are price takers

Short-run equilibrium:

• Firm produces where MR = MC
• Can make supernormal profit (if P \gt ATC), normal profit (if P = ATC), or loss (if P \lt ATC)

Long-run equilibrium:

• Only normal profit (P = ATC = MC)
• Firm produces at the minimum point of ATC (productive efficiency)
• P = MC (allocative efficiency)

Monopoly

Characteristics:

• Single seller
• Unique product (no close substitutes)
• High barriers to entry
• Price maker

Barriers to entry:

• Economies of scale
• Legal barriers (patents, licences)
• Control of essential resources
• Aggressive tactics (predatory pricing)

Monopoly vs Perfect Competition:

Feature	Perfect Competition	Monopoly
Price	Lower	Higher
Output	Higher	Lower
Efficiency	Both productive and allocative	Neither
Consumer surplus	Larger	Smaller
Deadweight loss	None	Present
Innovation	May lack incentive	May have incentive

warning

warning where MR = MC. Setting the highest price would reduce quantity sold too much and lower total revenue.

danger

danger

• Confusing a change in demand with a change in quantity demanded: A change in quantity demanded is caused by a price change and is a MOVEMENT ALONG the demand curve. A change in demand is caused by non-price factors (income, tastes, prices of related goods) and is a SHIFT of the entire demand curve. This distinction is fundamental and frequently tested.

• Confusing a movement along the supply curve with a shift of supply: An increase in price causes a movement ALONG the supply curve (quantity supplied increases). A change in production costs, technology, or number of firms causes the SUPPLY CURVE to SHIFT. Just like demand, movement along vs shift is a critical distinction.

• Assuming equilibrium price is always "fair": Market equilibrium is where quantity demanded equals quantity supplied. This is a positive (descriptive) outcome, not a normative (ethical) one. The equilibrium price may be too high for poor consumers to afford essential goods, which is why governments may intervene with price controls or subsidies.

• Misidentifying the effects of taxes and subsidies on equilibrium: A tax on producers shifts the supply curve LEFT (upward), increasing equilibrium price and decreasing quantity. A subsidy shifts supply RIGHT (downward), decreasing price and increasing quantity. The burden of a tax is shared between consumers and producers depending on the price elasticity of demand and supply.

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National Income Accounting

Measuring National Income

National income can be measured in three ways:

1. Output method: Sum of value added by all firms
2. Income method: Sum of all incomes (wages, rent, interest, profit)
3. Expenditure method: Sum of all spending

$\mathrm{GDP} = C + I + G + (X - M)$

Where:

• C = Consumption expenditure
• I = Investment expenditure
• G = Government expenditure
• X = Exports
• M = Imports

Key Measures

Measure	Definition
GDP (Gross Domestic Product)	Total value of goods and services produced within a country
GNP (Gross National Product)	GDP + Net income from abroad
NNP (Net National Product)	GNP - Depreciation
Per capita income	National income / Population

Limitations of GDP as a Measure of Welfare

• Does not account for leisure time
• Does not measure non-market activities (e.g., household work)
• Does not consider income distribution
• Does not reflect environmental degradation
• Does not account for improvements in quality of goods

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Inflation and Unemployment

Inflation

Inflation is a sustained increase in the general price level.

Causes:

• Demand-pull inflation: Aggregate demand exceeds aggregate supply
• Cost-push inflation: Increase in production costs (wages, raw materials)

Measurement:

• Consumer Price Index (CPI)
• GDP deflator

Unemployment

Type	Cause	Solution
Frictional	Time between jobs	Better job information
Structural	Mismatch of skills or location	Retraining, relocation
Cyclical	Insufficient aggregate demand	Fiscal/monetary policy

Phillips Curve

The Phillips curve suggests an inverse relationship between inflation and unemployment in the short run. Lower unemployment tends to be associated with higher inflation, and vice versa.

In the long run, the Phillips curve is vertical at the natural rate of unemployment (NRU), meaning there is no trade-off between inflation and unemployment.

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Government Policies

Fiscal Policy

Fiscal policy involves government decisions on taxation and spending to influence the economy.

Expansionary fiscal policy:

• Increase government spending
• Decrease taxes
• Used during recession to boost aggregate demand

Contractionary fiscal policy:

• Decrease government spending
• Increase taxes
• Used during inflation to reduce aggregate demand

Monetary Policy

Monetary policy involves the central bank's control of the money supply and interest rates.

Expansionary monetary policy:

• Lower interest rates
• Increase money supply
• Encourages borrowing and spending

Contractionary monetary policy:

• Raise interest rates
• Reduce money supply
• Discourages borrowing and spending

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Additional Practice Questions

More Exam-Style Problems

Question 4: A firm has fixed costs of USD 200 and variable costs given by VC = 10Q + 0.5Q$^2$. Find the output at which average total cost is minimised.

$TC = 200 + 10Q + 0.5Q^2$

$ATC = \frac{200}{Q} + 10 + 0.5Q$

To minimise ATC, take the derivative and set to zero:

$\frac{d(ATC)}{dQ} = -\frac{200}{Q^2} + 0.5 = 0$

$0.5 = \frac{200}{Q^2}$

$Q^2 = 400$

$Q = 20$

At Q = 20: ATC = 200/20 + 10 + 0.5(20) = 10 + 10 + 10 = USD 30.

Question 5: The demand function is $Q_D = 200 - 4P$ and the supply function is $Q_S = 2P - 40$. The government imposes a specific tax of USD 8 per unit. Calculate the tax revenue and deadweight loss.

Original equilibrium: $200 - 4P = 2P - 40$, $240 = 6P$, $P = 40$, $Q = 40$.

With tax: supply becomes $Q_S = 2(P - 8) - 40 = 2P - 56$

$200 - 4P = 2P - 56$

$256 = 6P$

$P = 42.67$ (price consumers pay)

$Q = 200 - 4(42.67) = 29.33$

Tax revenue $= 8 \times 29.33 = 234.67$

Deadweight loss $= \frac{1}{2} \times \mathrm{tax} \times (\mathrm{original Q} - \mathrm{new Q})$

$\mathrm{DWL} = \frac{1}{2} \times 8 \times (40 - 29.33) = \frac{1}{2} \times 8 \times 10.67 = 42.67$

Question 6: Explain why a monopoly causes allocative inefficiency.

A monopoly produces where MR = MC. Since the monopoly's MR curve lies below the demand curve (AR), the price charged is greater than MC (P \gt MC). This means the value consumers place on the last unit (P) exceeds the cost of producing it (MC). Society would benefit from more output, but the monopoly restricts output to maximise profit, creating a deadweight loss. In perfect competition, P = MC, which is allocatively efficient.

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Problem Set

Problem 1: Market Equilibrium with Shifts

Given $Q_D = 150 - 3P$ and $Q_S = 2P - 30$.

(a) Find the equilibrium price and quantity. (b) If demand increases by 60 units at every price (new $Q_D = 210 - 3P$), find the new equilibrium. (c) If both demand and supply increase by 60 units, what happens to equilibrium quantity? What about price?

Solution

(a) 150 - 3P = 2P - 30, 180 = 5P, P = 36. Q = 150 - 108 = 42.

(b) 210 - 3P = 2P - 30, 240 = 5P, P = 48. Q = 210 - 144 = 66.

Price rises from 36 to 48; quantity rises from 42 to 66.

(c) New supply: Q_S = 2P + 30. 210 - 3P = 2P + 30, 180 = 5P, P = 36. Q = 210 - 108 = 102.

Quantity rises (42 to 102), but price returns to 36. When both curves shift right by the same amount, price is unchanged and quantity increases.

If you get this wrong, revise: Changes in Equilibrium

Problem 2: PED and Total Revenue

A shop sells Good G at USD 20 per unit, selling 500 units per week. When the price is raised to USD 24, sales fall to 400 units per week.

(a) Calculate PED. (b) Did total revenue increase or decrease? (c) Should the shop raise or lower the price to maximise revenue?

Solution

(a) % change in Q = (400-500)/500 \times 100\% = -20\%. % change in P = (24-20)/20 \times 100\% = 20\%. PED = -20/20 = -1 (unit elastic).

(b) TR before = 20 \times 500 = 10,000. TR after = 24 \times 400 = 9,600. TR decreased by 400.

(c) Since demand is unit elastic (PED = -1), the shop is already at the revenue-maximising price. Raising or lowering the price would both decrease total revenue.

If you get this wrong, revise: PED and Total Revenue

Problem 3: Cross Elasticity

When the price of coffee rises by 10%, the quantity demanded of tea rises by 6%. When the price of milk rises by 15%, the quantity demanded of coffee falls by 3%.

(a) What is the relationship between coffee and tea? (b) What is the relationship between coffee and milk? (c) If the price of coffee is expected to rise, what should a tea producer do?

Solution

(a) XED = 6/10 = 0.6 \gt 0. Coffee and tea are substitutes.

(b) XED = -3/15 = -0.2 \lt 0. Coffee and milk are complements.

(c) A tea producer should increase production. The expected rise in coffee prices will shift demand for tea to the right (consumers substitute from coffee to tea), increasing both the price and quantity of tea.

If you get this wrong, revise: Cross Elasticity of Demand (XED)

Problem 4: Price Ceiling

The market for rental housing has demand $Q_D = 500 - 2P$ and supply $Q_S = 100 + 3P$ (quantity in units, price in USD hundred).

(a) Find the equilibrium rent and quantity. (b) The government imposes a rent ceiling of USD 40 (hundred). Find the resulting shortage. (c) What problems might arise?

Solution

(a) 500 - 2P = 100 + 3P, 400 = 5P, P = 80 (hundred). Q = 500 - 160 = 340.

(b) At P = 40: Q_D = 500 - 80 = 420. Q_S = 100 + 120 = 220. Shortage = 420 - 220 = 200 units.

(c) Problems: black market (landlords sublet at above-ceiling prices), reduced quality and maintenance (landlords cut costs), reduced supply in the long run (landlords convert properties), inefficient allocation (units not rented to those who value them most).

If you get this wrong, revise: Price Controls

Problem 5: Tax Incidence

Demand: $Q_D = 300 - 5P$. Supply: $Q_S = 4P - 60$. A specific tax of USD 6 per unit is imposed on producers.

(a) Find the original equilibrium. (b) Find the new equilibrium after the tax. (c) Calculate the burden on consumers and producers. (d) Who bears more of the tax burden and why?

Solution

(a) 300 - 5P = 4P - 60, 360 = 9P, P = 40. Q = 300 - 200 = 100.

(b) Supply shifts: Q_S = 4(P-6) - 60 = 4P - 84. 300 - 5P = 4P - 84, 384 = 9P, P = 42.67 (consumers pay). Producers receive 42.67 - 6 = 36.67. Q = 300 - 213.3 = 86.67.

(c) Consumer burden per unit = 42.67 - 40 = 2.67. Producer burden per unit = 40 - 36.67 = 3.33.

(d) Producers bear more of the burden (3.33 vs 2.67) because supply is relatively less elastic than demand (producers are less responsive to price changes than consumers).

If you get this wrong, revise: Tax Incidence (Burden)

Problem 6: Income Elasticity

When average income rises by 10%, the quantity demanded of bus rides falls by 5% while the quantity demanded of restaurant meals rises by 15%.

(a) Classify bus rides and restaurant meals by type of good. (b) During an economic recession (falling incomes), what happens to demand for each good? (c) Why is this distinction important for businesses?

Solution

(a) Bus rides: YED = -5/10 = -0.5 \lt 0. Inferior good. Restaurant meals: YED = 15/10 = 1.5 \gt 1. Luxury (normal) good.

(b) During a recession (falling incomes): Demand for bus rides increases (people switch from taxis to buses). Demand for restaurant meals decreases (people cut back on luxuries).

(c) Businesses need to anticipate how demand changes with the business cycle. Bus operators should prepare for higher demand during recessions; restaurants should plan for lower demand and may need to adjust pricing or offer promotions.

If you get this wrong, revise: Income Elasticity of Demand (YED)

Problem 7: Subsidy Analysis

Demand: $Q_D = 200 - 2P$. Supply: $Q_S = 3P - 80$. The government provides a subsidy of USD 5 per unit to producers.

(a) Find the original equilibrium. (b) Find the new equilibrium after the subsidy. (c) How much does the subsidy cost the government? (d) Who benefits more from the subsidy -- consumers or producers?

Solution

(a) 200 - 2P = 3P - 80, 280 = 5P, P = 56. Q = 200 - 112 = 88.

(b) Supply shifts down: Q_S = 3(P+5) - 80 = 3P - 65. 200 - 2P = 3P - 65, 265 = 5P, P = 53 (consumers pay). Producers receive 53 + 5 = 58. Q = 200 - 106 = 94.

(c) Government cost = 5 \times 94 = 470.

(d) Consumer benefit per unit = 56 - 53 = 3. Total consumer benefit = 3 \times 94 = 282. Producer benefit per unit = 58 - 56 = 2. Total producer benefit = 2 \times 94 = 188. Consumers benefit more (282 vs 188) because demand is more elastic than supply in this case.

If you get this wrong, revise: Subsidies

Problem 8: Negative Externality

A factory producing chemicals has MPC = 10 + Q. The marginal external cost is MEC = 8. Demand is P = 60 - Q.

(a) Find the market equilibrium output and price. (b) Find the socially optimal output and price. (c) Calculate the deadweight loss. (d) What per-unit tax would achieve the social optimum?

Solution

(a) Market: 10 + Q = 60 - Q, 2Q = 50, Q = 25. P = 35.

(b) Social optimum: MSC = MPC + MEC = 10 + Q + 8 = 18 + Q. 18 + Q = 60 - Q, 2Q = 42, Q = 21. P = 39 (price consumers pay). Producers receive 39 - 8 = 31.

(c) DWL = 0.5 \times 8 \times (25 - 21) = 0.5 \times 8 \times 4 = 16.

(d) Pigouvian tax = MEC = 8 per unit. This shifts the supply curve up from MPC to MSC.

If you get this wrong, revise: Market Failure

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Extended Problem Set: Advanced Demand and Supply Analysis

Problem 9: Simultaneous Demand and Supply Shifts with Algebra

The market for rice in Hong Kong has demand $Q_d = 400 - 2P$ and supply $Q_s = -80 + 4P$ (where $P$ is in HKD per kg and $Q$ is in thousand kg). Two events occur simultaneously: (i) a health report increases demand by 20% at every price, and (ii) a technological improvement increases supply by 30% at every price.

(a) Calculate the original equilibrium. (b) Calculate the new equilibrium after both shifts. (c) Calculate the percentage change in equilibrium price and quantity. (d) Decompose the price change into the portion due to the demand shift and the portion due to the supply shift.

Solution

(a) Original: $400 - 2P = -80 + 4P$. $480 = 6P$. $P^* = 80$. $Q^* = 400 - 160 = 240$.

(b) New demand: $Q_d' = 1.2(400 - 2P) = 480 - 2.4P$. New supply: $Q_s' = 1.3(-80 + 4P) = -104 + 5.2P$.

$480 - 2.4P = -104 + 5.2P$. $584 = 7.6P$. $P' = 76.84$. $Q' = 480 - 2.4(76.84) = 480 - 184.4 = 295.6$.

(c) Price change $= \frac{76.84 - 80}{80} \times 100\% = -3.95\%$. Quantity change $= \frac{295.6 - 240}{240} \times 100\% = 23.17\%$.

(d) If only demand shifted (supply unchanged): $480 - 2.4P = -80 + 4P$. $560 = 6.4P$. $P = 87.5$. Price effect of demand shift alone $= +87.5 - 80 = +7.5$.

If only supply shifted (demand unchanged): $400 - 2P = -104 + 5.2P$. $504 = 7.2P$. $P = 70$. Price effect of supply shift alone $= -80 + 70 = -10$.

Combined: $+7.5 - 10 = -2.5$ (approximately matches the actual $-3.16$; the difference is due to the non-linear interaction of the two shifts).

If you get this wrong, revise: Market Equilibrium

Problem 10: Agricultural Price Support with Buffer Stocks

The government wants to maintain a minimum price for rice at HK$100 per kg. Market demand is$Q_d = 500 - 3P$and supply is$Q_s = -100 + 4P$ (in thousand kg).

(a) Calculate the free market equilibrium. (b) Calculate the surplus created by the price support. (c) If the government buys the surplus, calculate the cost to the government. (d) If the government instead pays farmers a per-unit subsidy to reduce the market price to HK$80 (which would increase quantity demanded), calculate the subsidy rate and the cost to the government. Compare with the price support approach.

Solution

(a) $500 - 3P = -100 + 4P$. $600 = 7P$. $P^* = 85.71$. $Q^* = 500 - 3(85.71) = 242.9$.

(b) At $P = 100$: $Q_d = 500 - 300 = 200$. $Q_s = -100 + 400 = 300$. Surplus $= 300 - 200 = 100$ thousand kg.

(c) Government cost = 100 \times 100 = \text{HK}\10,000$thousand$= \text\\{HK\\}$10$ million.

(d) To achieve $P_b = 80$ for consumers: subsidy $s$ such that $P_s = 80 + s$ and $Q_d(80) = Q_s(80 + s)$.

$Q_d(80) = 500 - 240 = 260$. $Q_s(80 + s) = -100 + 4(80 + s) = 220 + 4s$.

$260 = 220 + 4s$. $4s = 40$. $s = 10$.

Government cost = 10 \times 260 = \text{HK}\2,600$thousand$= \text\\{HK\\}$2.6$ million.

Comparison: The subsidy approach (HK$2.6M) costs much less than the price support (HK$10M) and results in a higher quantity consumed (260 vs 200), generating more consumer surplus. However, the subsidy approach transfers money to consumers (lower prices) and producers (higher effective prices), while the price support transfers money to producers only (through government purchases of surplus).

If you get this wrong, revise: Government Price Controls

Problem 11: Tax Incidence with Different Elasticities

The government imposes a HK$20 per unit tax on smartphones. Demand:$Q_d = 300 - 2P$. Two supply scenarios: Supply A:$Q_s = -50 + 3P$(elastic supply). Supply B:$Q_s = -200 + 5P$ (more elastic supply).

(a) For each supply scenario, calculate the pre-tax and post-tax equilibrium, consumer burden, and producer burden. (b) Explain why the incidence differs between the two scenarios. (c) Calculate and compare the deadweight loss in each scenario. (d) What are the implications for tax policy design?

Solution

Supply A ($Q_s = -50 + 3P$):

Pre-tax: $300 - 2P = -50 + 3P$. $350 = 5P$. $P^* = 70$. $Q^* = 300 - 140 = 160$.

Post-tax: $300 - 2P_b = -50 + 3(P_b - 20) = -50 + 3P_b - 60 = -110 + 3P_b$.

$300 - 2P_b = -110 + 3P_b$. $410 = 5P_b$. $P_b = 82$. $P_s = 62$. $Q_t = 300 - 164 = 136$.

Consumer burden $= 82 - 70 = 12$ (60% of tax). Producer burden $= 70 - 62 = 8$ (40% of tax).

$DWL_A = 0.5 \times 20 \times (160 - 136) = 0.5 \times 20 \times 24 = 240$.

Supply B ($Q_s = -200 + 5P$):

Pre-tax: $300 - 2P = -200 + 5P$. $500 = 7P$. $P^* = 71.43$. $Q^* = 300 - 142.86 = 157.14$.

Post-tax: $300 - 2P_b = -200 + 5(P_b - 20) = -200 + 5P_b - 100 = -300 + 5P_b$.

$300 - 2P_b = -300 + 5P_b$. $600 = 7P_b$. $P_b = 85.71$. $P_s = 65.71$. $Q_t = 300 - 171.43 = 128.57$.

Consumer burden $= 85.71 - 71.43 = 14.28$ (71.4% of tax). Producer burden $= 71.43 - 65.71 = 5.72$ (28.6% of tax).

$DWL_B = 0.5 \times 20 \times (157.14 - 128.57) = 0.5 \times 20 \times 28.57 = 285.7$.

(b) Supply B is more elastic (flatter slope coefficient 5 vs 3), meaning producers are more responsive to price changes. With more elastic supply, producers bear a smaller share of the tax (28.6% vs 40%) because they can more easily reduce quantity in response to the lower net price. Consumers bear a larger share because they are relatively less responsive (same demand curve in both scenarios).

(c) DWL is larger with more elastic supply (285.7 vs 240) because the quantity reduction is larger when supply is more elastic. The tax creates more allocative inefficiency when either demand or supply is more elastic.

(d) Tax policy implications: To minimise deadweight loss, governments should tax goods with inelastic demand or supply (where the quantity response is small). This is the efficiency argument for taxing cigarettes, alcohol, and petrol (inelastic demand). Conversely, taxing goods with elastic demand or supply creates large DWL and is economically inefficient, though it may be justified on equity grounds.

If you get this wrong, revise: Tax Incidence and Elasticity

Problem 12: Price Ceiling with Quality Deterioration

A rent control law sets maximum rent at HK$15,000 per month for apartments. The free market equilibrium is HK$20,000 with 10,000 units rented. Demand: $Q_d = 18000 - 0.4P$. Supply: $Q_s = 2P - 30000$ (where $P$ is in HKD).

(a) Calculate the shortage created by the rent ceiling. (b) Calculate the change in consumer surplus, producer surplus, and DWL. (c) Landlords respond to the ceiling by reducing maintenance spending by HK$3,000 per unit per month. How does this quality deterioration affect the welfare analysis? (d) Explain the concept of "effective price" and why rent ceilings can make tenants worse off despite lower nominal rents.

Solution

(a) At $P = 15\,000$: $Q_d = 18000 - 6000 = 12\,000$. $Q_s = 30000 - 30000 = 0$.

This gives $Q_s = 0$, which means the supply curve must be recalibrated. Let me use: $Q_s = -6000 + 0.8P$.

At $P = 20\,000$: $Q_s = -6000 + 16000 = 10\,000 = Q^*$. $Q_d = 18000 - 8000 = 10\,000 = Q^*$. Good.

At $P = 15\,000$: $Q_d = 18000 - 6000 = 12\,000$. $Q_s = -6000 + 12000 = 6\,000$. Shortage $= 12\,000 - 6\,000 = 6\,000$ units.

Quantity traded $= 6\,000$ (the short side of the market).

(b) CS before $= 0.5 \times (45000 - 20000) \times 10000 = 0.5 \times 25000 \times 10000 = 125\,000\,000$.

CS after $= 0.5 \times (45000 - 15000) \times 6000 = 0.5 \times 30000 \times 6000 = 90\,000\,000$.

Wait -- the demand price at $Q = 6000$ is $P = (18000 - 6000)/0.4 = 30000$. So CS should include the area between the demand curve and the ceiling price up to $Q = 6000$:

CS after $= 0.5 \times (30000 - 15000 + 45000 - 15000) \times 6000 =$ No, this isn't right either.

CS after $= \int_0^{6000} (45000 - 0.4^{-1}(Q)) dQ - 15000 \times 6000$.

Demand inverse: $P = (18000 - Q)/0.4 = 45000 - 2.5Q$. At $Q = 6000$: $P = 45000 - 15000 = 30000$.

CS after $= 0.5 \times (45000 - 30000) \times 6000 + (30000 - 15000) \times 6000 = 0.5 \times 15000 \times 6000 + 15000 \times 6000 = 45\,000\,000 + 90\,000\,000 = 135\,000\,000$.

Hmm, this is larger than before, which is suspicious. Let me recalculate CS before.

CS before $= 0.5 \times (45000 - 20000) \times 10000 = 0.5 \times 25000 \times 10000 = 125\,000\,000$.

CS after $= 0.5 \times (45000 - 20000 + 30000 - 15000) \times 6000 =$ No, the correct CS is the area under the demand curve above the price, for the quantity actually consumed:

CS after $= 0.5 \times (30000 - 15000) \times 6000 + (45000 - 30000) \times 6000 = 45\,000\,000 + 90\,000\,000 = 135\,000\,000$.

Wait, that can't be right. The CS should be calculated as:

$CS = \int_0^{6000} (45000 - 2.5Q) dQ - 15000 \times 6000 = [45000Q - 1.25Q^2]_0^{6000} - 90\,000\,000 = (270\,000\,000 - 45\,000\,000) - 90\,000\,000 = 225\,000\,000 - 90\,000\,000 = 135\,000\,000$.

So CS increases from 125M to 135M? This is because the effective price for those who get apartments is lower (15,000 vs 20,000), and the demand price at Q=6000 (30,000) is very high. But this ignores the non-price rationing (queuing, bribery, discrimination) that determines which consumers actually get apartments. The measured CS assumes the consumers with the highest willingness to pay get the apartments, which may not be the case with non-price rationing.

PS before $= 0.5 \times (20000 - 7500) \times 10000 = 0.5 \times 12500 \times 10000 = 62\,500\,000$.

(Supply intercept: $0 = -6000 + 0.8P$, $P = 7500$.)

PS after $= 0.5 \times (15000 - 7500) \times 6000 = 0.5 \times 7500 \times 6000 = 22\,500\,000$.

DWL $= (125M + 62.5M) - (135M + 22.5M) = 187.5M - 157.5M = 30\,000\,000$.

(c) If landlords reduce maintenance by HK$3,000 per unit, the effective quality-adjusted rent for tenants is$15000 + 3000 = 18000$(the tenant pays 15,000 in cash but receives a lower-quality apartment worth 3,000 less). The true cost to tenants is HK$18,000, which is only HK$2,000 less than the free market rent of HK$20,000. The CS calculation overstates the benefit of the ceiling because it does not account for quality deterioration.

(d) The effective price of a rent-controlled apartment includes both the monetary rent and the non-monetary costs: search costs (time spent looking), waiting time (queueing for the limited supply), quality deterioration (poor maintenance), and side payments (key money, bribes). When these are included, the effective price may exceed the free market rent, making tenants worse off. This is a key insight of the economic analysis of rent control: the nominal price falls, but the total cost (including non-monetary costs) may rise.

If you get this wrong, revise: Price Controls and Welfare