Profit Maximization Day 2 Ap micro 10/13

Warm Up Kate’s Katering: Assume the catered meals industry is perfectly competitive. Her fixed cost is $100/day. Quantity of Meals VC FC TC AVC ATC MC $0 10 200 20 300 30 480 40 700 50 1,000

Quantity of Meals VC FC TC AVC ATC MC $0 $100 --- 10 200 100 300 20 30 400 15 480 580 16 19.33 18 40 700 800 17.50 22 50 1,000 1100

When is Production Profitable? Depends on economic profit: a measure based on the opportunity cost of resources used in the business -- TR minus explicit and implicit costs (benefits forgone in the next best use of the firms resources) Vs. Accounting profit = TR-TC (only explicit costs) We will assume that our cost totals include explicit and implicit costs, and profit totals are economic profit

Break Even Point Price, cost of bushel At point C (the minimum average total cost), the market price is $14 and output is 4 bushels of tomatoes (the minimum-cost output). $30 MC Minimum average total cost 18 A T C C Break even price 14 MR = P 1 2 3 4 5 6 7 Quantity of tomatoes (bushels) Minimum-cost output This is where MC cuts the ATC curve at its minimum. Minimum average total cost is equal to the firm’s break-even price.

Profitability Graph The farm is profitable because price exceeds minimum average total cost, the break-even price, $14. The farm’s optimal output choice is (E)  output of 5 bushels. The average total cost of producing bushels is (Z on the ATC curve) $14.40 Market Price = $18 Price, cost of bushel Minimum average total cost MC E $18 MR = P 14.40 Profit A T C 14 Z Break even price C The vertical distance between E and Z: farm’s per unit profit, $18.00 − $14.40 = $3.60 Total profit:5 × $3.60 = $18.00 1 2 3 4 5 6 7 Quantity of tomatoes (bushels)

Unprofitable Graph The farm is unprofitable because the price falls below the minimum average total cost, $14. The farm’s optimal output choice is (A)  output of 3 bushels. The average total cost of producing bushels is (Y on the ATC curve) $14.67 Market Price = $10 Price, cost of bushel Minimum average total cost MC A T C $14.67 Y 14 Break even price C Loss 10 MR = P The vertical distance between A and Y: farm’s per unit loss, $14.67 − $10.00 = $4.67 Total profit:3 × $4.67 = approx. $14.00 A 1 2 3 4 5 6 7 Quantity of tomatoes (bushels)

Price = $18: Firm produces 5 units, is profiting Price = $14: Firm produces 4, is breaking even Price = $12: Firm produces 3.5, is incurring a loss, will stay in business in short run, exits industry in long run Price = $10 or less: Firm exits industry immediately Price, cost of bushel Short-run individual supply curve MC $18 E A T C 16 A VC 14 C 12 B 10 A Minimum average variable cost 1 2 3 3.5 4 5 6 7 Quantity of tomatoes (bushels)

Profit, Break-Even, Loss, Shut Down Decisions Whenever P > ATC, the producer is profitable. Whenever P = ATC, the producer breaks even. Whenever AVC < P < ATC, the producer is unprofitable – should stay in business in the short run. Whenever P < AVC, the producer should shut down immediately.

Shut Down Vs. Loss in SR Scenario Our business has a fixed cost of $20,000 per year. We incur an economic loss of $10,000 per year. In the short run: If we stay in business, we owe $10,000. If we close down, we owe $20,000. What should we do? Scenario 2: Our business has a fixed cost of $8000 per year. We incur an economic loss of $10,000 per year. In the short run: If we stay in business, we lose $10,000. If we close, we owe $8000. What should we do?

Practice Problem Using the warm up: Quantity of Meals VC FC TC AVC ATC MC $0 $100 --- 10 200 100 300 20 30 400 15 480 580 16 19.33 18 40 700 800 17.50 22 50 1,000 1100

What is the break-even price? What is the shut-down price? Suppose that the price at which Kate can sell meals is $21 per meal. How many meals will she produce? In the short run, will Kate earn a profit? In the short run, should she produce or shut down? Suppose that the price falls to $17 per meal. How many meals will she produce? In the short run, will Kate earn a profit? Should she produce or shut down? Suppose the price falls to $13. In the short run, will Kate earn a profit? Should she produce or shut down?

What is the break-even price? $19.33 (min ATC) What is the shut-down price? $15 (min AVC) Suppose that the price at which Kate can sell meals is $21 per meal. In the short run, will Kate earn a profit? In the short run, should she produce or shut down? Will profit and produce Suppose that the price falls to $17 per meal. In the short run, will Kate earn a profit? Should she produce or shut down? Will not profit, still produce Suppose the price falls to $13. In the short run, will Kate earn a profit? Should she produce or shut down? Not profit, shut down now