AAEC 3315 Agricultural Price Theory

1. AAEC 3315Agricultural Price Theory CHAPTER 8 Profit Maximization The Case of One Variable Input in the Short-Run

2. Objectives To gain understanding of: • Profit Maximization • Total Revenue – Total Cost Approach • Per-Unit Output Approach • When should a firm produce? • Derivation of Supply

3. Profit Maximization:Total Revenue – Total Cost Approach •  = TR – TC • Firms will continue to expand production as long as increase in revenue is greater than increase in costs. • On the Diagram, the profit maximizing level of output is the level where the vertical difference between the TR and TC is the largest. With price of Y being $3/unit, Profits are maximized by producing 95 units (or slightly higher) of output.

4. Profit Maximization:Total Revenue – Total Cost Approach Stage I Max Profit Stage II Max Output Stage III

5. Profit Maximization:Per-Unit Output Basis • Most managers do not make decisions looking at TR and TC. Most decisions are made at the “margin.” • The output level that will maximize  is determined by comparing the amount that EACH ADDITIONAL unit of output adds to TR and TC. • Recall, Marginal Cost (MC) represents additional cost from producing an additional unit of output; and Marginal Revenue (MR) represents addition to TR from selling (producing) an additional (one more) unit of output, which is equal to the price of that output. • Thus, MC and MR can be used to determine profit maximizing level of output.

6. Determining  Max:Per-unit Output Basis • Firm will continue to expand production until added revenue received from additional unit of output sold (MR) is equal to the additional cost of producing that unit of output (MC), i.e., profit is maximized when MR = MC. With price of Y being $3/unit, Profits are maximized by producing 95 units (or slightly higher) of output.

7. Profit Maximization:Per-Unit Output Basis Stage I Max Profit Stage II Max Output Stage III

8. Profit Maximization:A Mathematical Example Suppose that a firm’s total cost function is TC = 400 + 3Q2 And the TR function is TR = 12 Q What is the profit maximizing level of output? Condition for profit maximization: MR = MC MR = ∂TR/∂Q = ∂(12Q)/∂Q = 12 MC = ∂TC/∂Q = ∂(400+3Q2)/∂Q = 6Q MR = MC => 12 = 6Q Q = 2

9. When the Firm Should Produce? Given price “P”, the AR and MR are given by the horizontal line at P. Profit is maximized by producing Q level of output, where MR = MC. AR = MR A P E B TR is given by the area PAQ0 D C TVC is given by the area DCQ0 TC is given by the area EBQ0 TFC is given by the area EBCD Profit is given by the area PABE 0 Q

10. When the Firm Should Produce? At P1, the firm is making profit P1 At P2, the firm is at the break-even point P2 P3 At P3, the firm continues to produce to minimize loss P4 At P4, the firm may continue to produce P5 At P5, the firm will close down 0 Q5 Q4 Q3 Q2 Q1 Thus, a profit maximizing firm will continue to produce as long as the price of the product is above the AVC.

11. When to Produce:A Mathematical Example • Suppose that a firm’s total cost function is TC = 400 + 3Q2. If the price of the product is $12.00; • What is the profit maximizing level of output? • At the profit max level of output, what are the firm’s TC, TVC, TFC, ATC, AVC, AFC, TR, and Profit? • Is the firm better off to shut down or operate? Why? • TC = 400 + 3Q2; TFC = 400, TVC = 3Q2 • AC = TC/Q = 400/Q + 3Q • MC = ∂TC/∂Q = 6Q • Price = AR = MR = 12 • TR = Price x Quantity = 12 Q • a) Profit max level of output: MC = MR or 6Q = 12 or Q = 2 • b) At Q = 2; TC = $412, TVC = $12, TFC = $400, ATC = $206, AVC = $6, AFC = $200, TR = $24, Profit = -$388 • c) Since Price ($12) > AVC ($6) the firm is better off to produce. But note that the firm is making a loss and that is because its ATC is greater than Price. The firm is better off to operate because if it does not then it will loose $400 (fixed cost) rather than #388.

12. Supply • Supply is a direct price and quantity relationship indicating how suppliers (producers, sellers, & mgrs) of a product respond to differing price levels. • It states what suppliers are WILLING and ABLE to supply at a given price.

13. Derivation of Supply Curves • Supply curve for the individual firm is based on the cost structure of the firm & how managers respond to alternative product prices as they attempt to maximize profits. • We discussed earlier that profit maximizing firms will shut down if the price of the product falls below the AVC. P1 Q1

14. Derivation of Supply Curves • This implies that the MC curve above AVC represents the firm’s supply curve. P1 Q1

15. Law of Supply • The Law of Supply says that the quantity of goods &/or services offered will vary DIRECTLY with the price. • Price increase will result in an increase in quantity supplied. • Price decrease will result in a decrease in quantity supplied. • The amount of increase or decrease, however, depends on the Elasticity of Supply. Price S P3 P2 P1 Q1 Q2 Q3 Output