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### 040513

1. 1. Marginal Revenue & Marginal Cost April 5, 2013
2. 2. Announcements• 150 People are enrolled• As of last class, 50 had signed up to “follow” on website. econ2ucsd.wordpress.com• 45 had clickers. Today we have ___. (Freq. BB)• Takeaway: I need to give you better incentives.• Get a clicker and register by Monday, +5% extra credit on Midterm.• If you still haven’t registered by Monday, I will give more positive incentives to those who have.
3. 3. Last Class• Finished our review of producer and consumer surplus from Econ 1.• Today, final Econ 1 review: The firm. – Marginal Revenue – Marginal Cost – Profit Maximization• Will make use of clickers to see if we are following the material.
4. 4. Learning Goals for Today• Calculate marginal revenue equation for given market demand – Derive total revenue, and connection with marginal revenue• Discern what a firm’s marginal costs are, and relate these to marginal revenue – Derive total cost as a function of capital and wage inputs, and connection with marginal revenue
5. 5. Total Revenue (TR)• The total income a firm receives for selling its goods.• Determined by Demand line: TR=PDQ.• If PD=a-bQ, and we only know Q, can we determine TR?• YES. TR=PDQ=(a-BQ)Q
6. 6. Total Revenue (TR) PQ PD TR 100 10 0 81 8 PD=10-2Q 62 6 43 4 24 2 D Q5 0 0 1 2 3 4 5
7. 7. Total Revenue (TR) PQ PD TR 100 10 0 81 8 8 PD=10-2Q 62 6 43 4 24 2 D Q5 0 0 1 2 3 4 5
8. 8. Total Revenue (TR) PQ PD TR 100 10 0 81 8 8 PD=10-2Q 62 6 12 43 4 24 2 D Q5 0 0 1 2 3 4 5
9. 9. Total Revenue (TR) PQ PD TR 100 10 0 81 8 8 PD=10-2Q 62 6 12 43 4 12 24 2 D Q5 0 0 1 2 3 4 5
10. 10. Total Revenue (TR) PQ PD TR 100 10 0 81 8 8 PD=10-2Q 62 6 12 43 4 12 24 2 8 D Q5 0 0 1 2 3 4 5
11. 11. Marginal Revenue• Added Revenue from immediate next unit of goods sold• MR(Q) = TR(Q) – TR(Q-1)• For instance, if TR from 3 sold is 10, and TR from 4 sold is 12, then MR(Q=4)=2.
12. 12. Marginal Revenue (MR)Q PD TR MR Graphical0 10 0 x x1 8 82 6 123 4 124 2 85 0 0
13. 13. Marginal Revenue (MR)Q PD TR MR Graphical0 10 0 x x1 8 8 8-0=82 6 123 4 124 2 85 0 0
14. 14. Marginal Revenue (MR)Q PD TR MR Graphical0 10 0 x x1 8 8 8-0=82 6 12 12-8=4 -3 4 124 2 85 0 0
15. 15. Marginal Revenue (MR)Q PD TR MR Graphical0 10 0 x x1 8 8 8-0=82 6 12 12-8=4 -3 4 12 12-12=0 -4 2 85 0 0
16. 16. Marginal Revenue (MR)Q PD TR MR Graphical0 10 0 x x1 8 8 8-0=82 6 12 12-8=4 -3 4 12 12-12=0 -4 2 8 8-12=-4 -5 0 0
17. 17. Marginal Revenue (MR)Q PD TR MR Graphical0 10 0 x x1 8 8 8-0=82 6 12 12-8=4 -3 4 12 12-12=0 -4 2 8 8-12=-4 -5 0 0 0-8=-8 -
18. 18. Marginal Revenue Can Be Negative PQ PD TR MR 100 10 0 x PD=10-2Q1 8 8 8 D2 6 12 4 Q 1 2 3 4 53 4 12 0 -84 2 8 -45 0 0 -8
19. 19. Why Does This Make Sense?If PD=a-bQ, TR=PDQ=aQ-bQ2, inverse quadratic equation. TR=PDQ TR TR Increasing Decreasing (1) When TR is increasing, MR is positive. (2) When TR is decreasing, MR is negative. P PD=a-bQ (3) However, Be careful to notice that MR is always decreasing. Q
20. 20. Theorem for when MR=0• If PD=a-bQ, then MR=0 when Q=(1/2)*(a/b). TR=PDQ Q P a PD=a-bQ Q (1/2)* b/a b/a
21. 21. Putting it all together. TR=PDQ Q P a PD=a-bQ Q (1/2)* b/a b/a MR -a
22. 22. PD=8-1/8Q. For which Q is MR positive?A. Q= 0 to 8B. Q= 8 to 16C. Q = 0 to 64D. Q = 0 to 32
23. 23. Answer: D• Theorem: If PD=a-bQ, MR intersects Q axis at (1/2)*a/b.• Here, PD=8-1/8Q.• So, (1/2)*a/b=(1/2)*8/(1/8)• Recall, 8/(1/8) = 8 * 8.• So, MR intersects Q axis at Q=1/2*64=32.• Correct answer: Positive on [0,32).
24. 24. Total Cost• Total cost is the dollar value of inputs necessary to produce some amount Q.• Say I use one unit of labor to produce Q units of output and the wage rate is w. Total cost of producing Q units is w.• Say I use one unit of capital to produce Q units of output and the rental rate is r. Total cost of producing Q units is r.
25. 25. ExampleWe consider a business that takes labor as the only input.Say the wage rate is w=\$10/hr, and there is diminishing marginal product of laborProducing Q Requires how many labor hours? TC MC0 0 0 01 0.2 (+0.2 hrs)2 0.6 (+0.4 hrs)3 1.2 (+0.6 hrs)4 2 (+0.8 hrs)5 3 (+1 hrs)
26. 26. ExampleWe consider a business that takes labor as the only input.Say the wage rate is w=\$10/hr, and there is diminishing marginal product of laborProducing Q Requires how many labor hours? TC MC0 0 0 01 0.2 (+0.2 hrs) 22 0.6 (+0.4 hrs) 63 1.2 (+0.6 hrs) 124 2 (+0.8 hrs) 205 3 (+1 hrs) 30
27. 27. ExampleWe consider a business that takes labor as the only input.Say the wage rate is w=\$10/hr, and there is diminishing marginal product of laborProducing Q Requires how many labor hours? TC MC0 0 0 01 0.2 (+0.2 hrs) 2 22 0.6 (+0.4 hrs) 6 43 1.2 (+0.6 hrs) 12 64 2 (+0.8 hrs) 20 85 3 (+1 hrs) 30 10
28. 28. Think• How does the marginal cost of a unit of production relate to the minimum amount you would be willing to accept for a unit of that good?
29. 29. Marginal Cost is AlsoA. The supply lineB. The demand lineC. The marginal revenue lineD. The marginal product line
30. 30. Answer: A• The supply line is the schedule of reservation prices, i.e., the minimum the seller is willing to accept for a given Q.• Surely, the seller will never accept less than MC.
31. 31. MR and MC. Putting the Two Examples together: Profits.Q PD MR MC=PS Profit0 10 x 01 8 8 22 6 4 43 4 0 64 2 -4 85 0 -8 10
32. 32. MR and MC. Putting the Two Examples together: Profits.Q PD MR MC=PS Profit0 10 x 01 8 8 2 62 6 4 4 03 4 0 6 -64 2 -4 8 -125 0 -8 10 -18
33. 33. Under perfect competition, P* is the market price. What price would aprofit-maximizing firm charge if there were no competition? PA. PA PA PS=MCB. PB PBC. PC P*D. PD(=0) PCE. P* PD PD Q MR
34. 34. Answer: Save for Next Class• We will begin our discussion here on Monday.• Make sure to bring Problem Set 1!• Check website for updates.