Producer's equilibrium: the MR–MC approach
Profit (π) = TR − TC. A firm wants maximum profit.
Producer's equilibrium is the output where profit is maximum. Conditions:
- MR = MC.
- MC is rising at that output (MC cuts MR from below). In other words, after this point MC > MR.
Reason: if MR > MC, one more unit adds more to revenue than to cost, so produce more. If MR < MC, the last unit lowers profit, so produce less.
| q | MR (= P) | MC | Profit added (MR − MC) |
|---|---|---|---|
| 1 | 50 | 40 | 10 |
| 2 | 50 | 30 | 20 |
| 3 | 50 | 20 | 30 |
| 4 | 50 | 30 | 20 |
| 5 | 50 | 50 | 0 |
| 6 | 50 | 70 | −20 |
Equilibrium at q = 5. The same point is where TR − TC is largest (TR − TC approach).
Supply and market supply
Supply = the quantity of a good a firm is willing and able to offer for sale at each price in a given period. Stock is the total amount held; supply is only the part offered at a price.
Market supply = sum of the supply of all firms at each price (horizontal summation).
| Price ₹ | Firm A | Firm B | Market |
|---|---|---|---|
| 4 | 2.5 | 0 | 2.5 |
| 6 | 5 | 3 | 8 |
| 8 | 7.5 | 6 | 13.5 |
| 10 | 10 | 9 | 19 |
Determinants of supply
- Own price: higher price, more supplied (law of supply).
- Prices of inputs: costlier inputs raise cost, supply falls.
- Technology: better technology lowers cost, supply rises.
- Taxes and subsidies: a unit tax raises cost (supply falls); a subsidy lowers cost (supply rises).
- Prices of other goods: if wheat price rises, a farmer may shift land from rice, so rice supply falls.
- Number of firms: more firms, more market supply.
- Goals of the firm and expectations: expecting higher prices tomorrow, a firm may hold back supply today.
Supply schedule, supply curve and law of supply
A supply schedule lists prices and quantities supplied; its graph is the supply curve, which usually slopes upward.
Law of supply: other things being equal, quantity supplied rises when price rises and falls when price falls. Reason: a higher price makes it profitable to produce units whose MC is higher. Under perfect competition, the firm's supply curve is the rising part of its MC curve above minimum AVC.
Movement along vs shift of the supply curve
| Movement along | Shift |
|---|---|
| Cause: own price changes | Cause: any other factor changes |
| Expansion (price up, more supplied) / contraction (price down, less supplied) | Increase (right shift) / decrease (left shift) |
Right shift: better technology, cheaper inputs, subsidy, more firms. Left shift: costlier inputs, new tax, fewer firms, price of another good rises.
Price elasticity of supply (percentage method)
Es = % change in quantity supplied ÷ % change in price = (ΔQ/ΔP) × (P/Q), using original P and Q. Es is positive because price and quantity supplied move together.
- Es = 0: perfectly inelastic (vertical).
- Es < 1: inelastic (a straight line through the quantity axis).
- Es = 1: unitary (any straight line through the origin).
- Es > 1: elastic (a straight line through the price axis).
- Es = ∞: perfectly elastic (horizontal).
Es depends on time available, nature of the good (perishable goods are less elastic), cost of increasing output and spare capacity.
Try it at home
Ask a local fruit seller: "If the price of mangoes went up by ₹20 a kilo tomorrow, would you bring more? How much more next week?" Write the % changes and work out Es for tomorrow and for next week. Why is next week's Es bigger?
Key formulas and definitions
- Profit = TR − TC
- Equilibrium: MR = MC and MC rising (MC > MR after it)
- Market supply = Σ firm supply at each price
- Es = (% ΔQs) ÷ (% ΔP) = (ΔQ/ΔP) × (P/Q)
- Line through origin: Es = 1; meets price axis: Es > 1; meets quantity axis: Es < 1
Worked examples
1. Price ₹50. MC of units 1 to 6: 40, 30, 20, 30, 50, 70. Find the equilibrium output.
MR = MC = 50 at q = 5 and MC is rising there. So q = 5.
2. MR = MC = 30 at q = 2 (MC falling) and at q = 4 (MC rising). Which is equilibrium?
q = 4, because MC must be rising. At q = 2 producing more still adds profit.
3. Price rises from ₹10 to ₹12; quantity supplied rises from 100 to 130. Find Es.
%ΔQ = 30%, %ΔP = 20%. Es = 30/20 = 1.5 (elastic).
4. Es = 2. Price rises by 5%. Quantity supplied was 400. Find the new quantity.
%ΔQ = 2 × 5 = 10% = 40. New quantity = 440.
5. Es = 0.5. Quantity supplied rises from 200 to 220. By what % did price rise?
%ΔQ = 10%. %ΔP = 10/0.5 = 20%.
6. The government gives a subsidy on fertiliser. What happens to wheat supply?
Cost of production falls, so supply increases: the supply curve shifts to the right.
Common mistakes
- Stopping at the first point where MR = MC even though MC is falling there.
- Calling a rise in quantity supplied due to a higher price an "increase in supply". It is an expansion (movement along).
- Using the new values as the base in the percentage method. Use the original P and Q.
- Thinking every straight-line supply curve has Es = 1. Only lines through the origin do.