relationships between different markets: joint supply

Cambridge International AS & A Level Economics (9708) – Joint Supply and Syllabus Overview

1. Foundations of Economic Thinking

• Scarcity & Choice: Resources are limited; societies must decide how to allocate them.
• Opportunity Cost: The value of the next best alternative foregone when a choice is made.
• Factors of Production: Land, labour, capital, entrepreneurship.
• Economic Systems: Market, command, mixed economies – how societies organise production and distribution.
• Production Possibility Curve (PPC):
  • Shows maximum feasible output of two goods.
  • Points on the curve = efficient use of resources; inside = under‑utilisation; outside = unattainable.
  • Joint supply is illustrated by a shift of the PPC outward along a ray that reflects simultaneous increases in two outputs.
• Classification of Goods (relevant for welfare analysis):
  • Private vs. public goods
  • Merit vs. demerit goods
  • Normal vs. inferior goods

2. Demand and Supply – The Price System

2.1 Demand

• Law of demand: ceteris paribus, higher price → lower quantity demanded.
• Determinants of demand: income, tastes, prices of related goods, expectations, number of buyers.
• Shift vs. movement:
  • Shift – change in a determinant (e.g., income rise → demand curve moves right).
  • Movement – change in price along the same curve.

2.2 Supply

• Law of supply: ceteris paribus, higher price → higher quantity supplied.
• Determinants of supply: input prices, technology, expectations, number of sellers, taxes/subsidies.
• Shift vs. movement – analogous to demand.

2.3 Market Equilibrium

• Equilibrium where quantity demanded = quantity supplied.
• Disequilibrium: surplus (price above equilibrium) or shortage (price below equilibrium) → price adjustments.

2.4 Elasticities

Elasticity	Formula	Interpretation
Price Elasticity of Demand (PED)	\(\displaystyle \frac{\% \Delta Q_D}{\% \Delta P}\)	‑ >1 = elastic, =1 = unit‑elastic, <1 = inelastic.
Price Elasticity of Supply (PES)	\(\displaystyle \frac{\% \Delta Q_S}{\% \Delta P}\)	Higher PES when producers can vary output easily.
Income Elasticity of Demand (YED)	\(\displaystyle \frac{\% \Delta Q_D}{\% \Delta Y}\)	Positive = normal good, negative = inferior good.
Cross‑price Elasticity of Demand (XED)	\(\displaystyle \frac{\% \Delta Q_{D\,X}}{\% \Delta P_{Y}}\)	Positive = substitutes, negative = complements.

2.5 Consumer & Producer Surplus

• Consumer Surplus (CS): Area between demand curve and market price up to the quantity bought.
• Producer Surplus (PS): Area between supply curve and market price up to the quantity sold.
• Welfare change = ΔCS + ΔPS (ignoring externalities & government revenue).
• Numerical example (AS‑level style):
  1. Demand: \(Q_D = 100 – 2P\)
  2. Supply: \(Q_S = 20 + 3P\)
  3. Equilibrium \(P = 16,\; Q = 68\).
  4. CS = \(\frac{1}{2}\times 68 \times (36 – 16)=680\); PS = \(\frac{1}{2}\times 68 \times (16 – 6.7)=630\).

3. Joint Supply – Linking Two Markets

3.1 Definition

• Joint supply occurs when a single production process yields two (or more) distinct outputs.
• The quantity supplied of each output is inter‑dependent because the outputs are produced together.
• A change in the price of one product can shift the supply curve of the other product.

3.2 Theoretical Framework

Assume a firm produces outputs X and Y using the same technology and inputs.

Profit‑maximising condition (price ratio = marginal‑cost ratio):

\[\frac{P_X}{P_Y}= \frac{MC_X}{MC_Y}\]

Because the marginal cost of an additional unit is identical for both outputs (MC_X = MC_Y), the condition simplifies to:

\[\frac{P_X}{P_Y}=1 \quad\Longrightarrow\quad P_X = P_Y\]

Consequences:

• If P_X rises, the firm expands total output, shifting the supply curve of Y rightward.
• If P_X falls, total output contracts, shifting the supply of Y leftward.

3.3 Interaction of Two Markets (Syllabus 2.4)

1. Price change in market A alters the profit‑maximising output level.
2. Supply curve in market B shifts (right if price of A rises, left if it falls).
3. New equilibrium in market B changes its price, quantity, CS and PS.

3.4 Welfare Effects (Syllabus 2.5)

• Right‑ward shift of supply in market B:
  • Price falls → CS ↑ (larger area under demand).
  • PS may rise if marginal cost is unchanged; otherwise it depends on the cost of producing the extra joint output.
• Left‑ward shift of supply in market B:
  • Price rises → CS ↓, PS may rise if producers capture higher prices.
• Overall welfare impact depends on the relative size of the cost change versus the price change.

3.5 Diagrammatic Representation

Use a two‑panel diagram:

1. Panel 1 – Market for Product A: Original supply S_A. A rise in P_B shifts S_A right to S'_A, leading to lower P_A and higher Q_A.
2. Panel 2 – Market for Product B: Original supply S_B. The same rise in P_B causes a movement up along S_B (higher price, higher quantity).

3.6 Real‑World Case Studies

• Beef and Leather: Higher world beef prices encourage larger herds; more hides are produced, shifting the leather supply curve rightward, lowering leather prices and increasing consumer surplus.
• Crude Oil and Natural Gas: Extraction of natural gas is often a by‑product of oil drilling. A tax on oil reduces output, shifting the gas supply curve leftward and raising gas prices.
• Cotton and Seed Oil: An increase in cotton prices raises the incentive to grow cotton, which also yields more cottonseed; the supply of cottonseed oil expands, lowering its price.

3.7 Government Intervention and Spill‑over Effects (Syllabus 3.2)

Intervention	Direct effect on the targeted product	Indirect effect on the related product
Specific tax on Product A	Increases producers’ marginal cost → supply of A shifts left; price rises, quantity falls.	Joint output falls → supply of Product B shifts left; its price rises and quantity falls.
Subsidy to Product B	Lowers effective marginal cost of B → supply of B shifts right; price falls, quantity rises.	Higher joint output → supply of Product A shifts right; its price falls and quantity rises.
Export quota on Product A	Limits foreign sales → domestic supply of A falls, raising domestic price.	Reduced joint output → supply of Product B shifts left, raising its price.

4. Reasons for Government Micro‑intervention (Syllabus 3.1)

• Market Failure:
  • Public goods (non‑rival, non‑excludable)
  • Externalities (positive & negative)
  • Merit & demerit goods
  • Information asymmetry
• Equity & Redistribution:
  • Progressive taxation, welfare transfers, minimum wage.
• Stabilisation of Prices:
  • Price controls (ceilings/floors), buffer stocks.

5. Inequality and Distribution (Syllabus 3.3)

• Measures of inequality: Gini coefficient, Lorenz curve.
• Policy tools:
  • Direct: progressive income tax, social security benefits.
  • Indirect: subsidies to low‑income groups, public provision of education & health.
• Welfare impact: transfers raise CS of low‑income households; possible PS loss for higher‑income producers, but overall welfare can rise if the marginal utility of income is higher for the poor.

6. Macroeconomics Overview (AS & A‑Level)

6.1 National Income Accounting (Syllabus 4.1‑4.3)

• GDP (Nominal): Sum of final goods & services produced in a year, measured at current market prices.
• Alternative measures: GNP, NNI, Net Domestic Product (NDP).
• Components of GDP (expenditure approach): \(GDP = C + I + G + (X-M)\).
• Income approach: wages, rent, interest, profits.
• Production approach: value added at each stage.
• Limitations: underground economy, non‑market services, environmental degradation.

6.2 Circular Flow of Income (Syllabus 4.4)

• Two‑sector model (households ↔ firms) – factor markets and product markets.
• Three‑sector model adds government; four‑sector adds foreign sector.
• Leakages (savings, taxes, imports) vs. injections (investment, government spending, exports).

6.3 Aggregate Demand & Aggregate Supply (AD/AS) (Syllabus 5.1‑5.4)

• Aggregate Demand (AD): total spending on domestically produced goods at each price level.
• Determinants: consumption, investment, government spending, net exports, expectations.
• Aggregate Supply (AS):
  • Short‑run AS (SRAS): upward sloping – prices of some inputs are sticky.
  • Long‑run AS (LRAS): vertical at full‑employment output.
• Equilibrium: intersection of AD and SRAS; shifts cause changes in output, price level, and unemployment.
• Policy analysis: fiscal & monetary actions move AD; supply‑side reforms shift LRAS.

6.4 Macro‑policy Objectives (Syllabus 5.5‑5.6)

• Economic growth – increase in potential output (LRAS rightward).
• Low unemployment – moving economy toward the natural rate.
• Price stability – avoiding inflationary or deflationary gaps.

7. Macro‑policy Instruments (Syllabus 5.2‑5.5)

7.1 Fiscal Policy

• Government spending (G) and taxation (T) directly affect AD.
• Expansionary fiscal policy: increase G or cut T → AD shifts right.
• Contractionary fiscal policy: decrease G or raise T → AD shifts left.
• Multiplier effect: \(\displaystyle k = \frac{1}{1-MPC}\) (simple model) – explains amplified impact on output.

7.2 Monetary Policy

• Controlled by the central bank (e.g., Bank of England, Federal Reserve).
• Instruments: open‑market operations, policy interest rate, reserve requirements.
• Expansionary: lower interest rates → investment ↑, consumption ↑ → AD rightward.
• Contractionary: raise rates → AD leftward.
• Liquidity trap: when interest rates are already near zero, monetary policy loses effectiveness.

7.3 Supply‑Side Policies (Syllabus 5.6)

• Goal: shift LRAS rightward, increasing potential output.
• Examples: investment in education & training, deregulation, tax incentives for R&D, infrastructure development.
• Short‑run trade‑off: may increase unemployment while reforms are implemented.

8. International Trade & Balance of Payments (Syllabus 6.1‑6.5)

8.1 Comparative & Absolute Advantage

• Absolute advantage: producing more output per unit of input than another country.
• Comparative advantage: lower opportunity cost; basis for mutually beneficial trade.
• Gains from trade: higher consumption possibilities, illustrated by production‑possibility frontiers.

8.2 Terms of Trade (ToT)

• ToT = (Export price index ÷ Import price index) × 100.
• Improvement → country can import more for a given quantity of exports.

8.3 Protectionist Instruments

Instrument	Purpose	Effect on Domestic Market
Tariff	Raise price of imports	Domestic price ↑, domestic output ↑, consumer surplus ↓, government revenue ↑.
Quota	Limit quantity of imports	Similar to tariff but creates scarcity rents.
Subsidy to exporters	Make exports more competitive	Export price falls, foreign demand rises; cost to government.
Import licence	Administrative control	Can be used to protect infant industries.

8.4 Balance of Payments (BoP)

• Current account: trade in goods & services, primary income, secondary income.
• Capital account: transfers of capital assets.
• Financial account: foreign direct investment, portfolio investment, reserve assets.
• BoP must balance (excluding statistical discrepancies); a deficit in the current account must be financed by a surplus in the capital/financial account or by drawing down reserves.

9. Joint Supply – Integrated Review (Linking Micro & Macro)

• Jointly‑supplied outputs affect the composition of a country’s export basket (e.g., oil & natural gas).
• Price shocks in one jointly‑supplied commodity can generate terms‑of‑trade fluctuations, influencing the current account.
• Government policies targeting one component (tax, subsidy, quota) have spill‑over effects on the other component, altering both micro‑level welfare and macro‑level aggregates such as GDP and the BoP.

10. Summary of Key Points

• Joint supply links two markets through a common production process; price changes in one market shift the supply curve of the other.
• Welfare effects are captured by changes in consumer and producer surplus; the net effect depends on cost changes.
• Government intervention in one market creates spill‑over effects on the related market – a crucial consideration for policy design.
• The broader syllabus requires understanding of:
  • Basic economic concepts, demand‑supply mechanics, elasticities, and surplus.
  • Reasons for and types of micro‑intervention, plus inequality concerns.
  • Macroeconomic fundamentals (GDP, AD/AS, macro‑policy) and international trade dynamics.

11. Practice Questions

1. Explain, using the profit‑maximising condition, how a specific tax on crude oil would affect the supply of natural gas. Include a diagram of the two linked markets.
2. Draw and label a two‑panel diagram to illustrate the impact on the leather market when the world price of beef falls. Explain the resulting changes in CS and PS in both markets.
3. Discuss the advantages and disadvantages for a government that subsidises timber production, taking into account its joint supply with pulp. Evaluate the welfare effects on consumers, producers and the state’s budget.
4. Using the AD/AS framework, analyse how a rise in the world price of a jointly‑supplied export (e.g., oil) can affect a small open economy’s output, price level and current account.
5. Calculate the price elasticity of demand for a good whose quantity demanded falls from 120 units to 90 units when its price rises from £8 to £10. Interpret the result.