1. September 19, 2009Section 4 Section Notes1 EWMBA201A Eva Vivalt

2. September 19, 2009Section 4 Section Notes2 Administrative Stuff 1.Recap of evaluations: 1.More of everything: intuition (helping with thought problems), numbers problems, extra problems, real-world examples. 2.Questions that are less crucial can be saved for after class. 3.Extra time after class. 4.I’ll distribute a pre-exam guide with more sample problems to work through and if you have questions on them you can ask me in office hours after section. 2.Sunk costs and Mid-term

3. September 19, 2009Section 4 Section Notes3 Recap of Costs Sunk Costs “Don’t worry about things you cannot change” Opportunity Costs “Always know what ALL your options are” Over the relevant time horizon… Total Costs: C(q) Fixed Costs: Not dependant on quantity produced: C(0) Variable Costs: C(q)-C(0) Marginal Costs: Cost of increasing q by a small amount: dC(q)/dq Average Total Costs: C(q)/q Average Variable Costs: vC(q)/q

4. September 19, 2009Section 4 Section Notes4 All the calculus it might be helpful to know Derivative of A + BQ + CQ 2 = B + 2CQ To minimize or maximize something: –1) Take its derivative (with respect to whatever it is that we are choosing, e.g. quantity to produce). –2) Set it equal to 0. –3) Solve for what we are choosing (e.g. Q).

5. September 19, 2009Section 4 Section Notes5 Thought Exercise What’s the difference between average cost and marginal cost? Between average variable cost and marginal cost?

6. September 19, 2009Section 4 Section Notes6 Thought Exercise What’s the difference between average cost and marginal cost? Between average variable cost and marginal cost? Marginal cost is the incremental cost of producing an additional unit. Average cost is the per unit cost of production, over all units produced. Side: average total cost divides both variable and fixed costs over the total production. Average variable cost averages only variable costs over the output. Marginal cost looks only at the cost of producing an extra unit. Average variable cost is the average variable cost across all output at a certain level.

7. September 19, 2009Section 4 Section Notes7 What do these functions look like? Cost ($) Variable Cost Total Cost Q Fixed Cost

8. September 19, 2009Section 4 Section Notes8 What do these functions look like? Cost ($) ATC MC AVC Q

9. September 19, 2009Section 4 Section Notes9 Why do we care what these look like? Knowing what things look like, what they include, and understanding how the curves relate to each other is helpful for building intuition, which is key to answering thought questions (or any questions). E.g. tax question on midterm – if you read the question carefully, and you understand the demand and supply curves, you should be able to modify their equations properly.

10. September 19, 2009Section 4 Section Notes10 Question 2 on problem set A) To minimize total costs, with C(Q)=405+20Q+5Q 2 we set Q=? Then profits = 120*(0)-(405+20*(0)+5(0) 2 ) = -405 B) To maximize sales, assuming that everything produced will be bought, produce the maximum possible: Q = 100. Then profits = 120*100-(405+20*100+5*100 2 ) = -40,405

11. September 19, 2009Section 4 Section Notes11 C) To minimize ATC, differentiate with respect to quantity (the thing that we are picking) and set that equal to 0: (Notation: ATC=AC, TC=C) ATC=TC/Q=405/Q+20+5Q = 405*Q -1 +20+5Q Differentiating: -405*Q -2 +5 Setting it equal to 0: -405*Q -2 +5=0 Solving: -405*Q -2 =-5  405/5=Q 2  Q=9

12. September 19, 2009Section 4 Section Notes12 Alternative way for C: We know ATC=MC at the minimum of ATC. We also know ATC=TC/Q=405/Q+20+5Q = 405*Q -1 +20+5Q. We also know MC=derivative of TC with respect to Q=20+10Q.  405*Q -1 +20+5Q=20+10Q  405*Q -1 =5Q  405=5Q 2  Q=9

13. September 19, 2009Section 4 Section Notes13 D) To maximize profits under perfect competition, set MC=price. MC = 20 + 10Q P = 120  20 + 10Q = 120  Q = 10 Thought question: why is this higher than the Q we found in part C?

14. September 19, 2009Section 4 Section Notes14 What does MC actually look like for this question? You check this later (analogous problem later this section): Does this industry have economies of scale or diseconomies of scale?

15. September 19, 2009Section 4 Section Notes15 Question 3 on problem set A) TR = P(Q)*Q = 100Q-Q 2 MR = dTR/dQ = 100-2Q When you’re a monopoly, max profits by setting MC=MR. Remember MC=dTC/dQ=10.  10=100-2Q  Q=45 Profit = TR – TC = P(Q)*Q – (100 + 10Q) = 55*45 – (100+10*45) = 1925

16. September 19, 2009Section 4 Section Notes16 B) We still want MC = MR. Can we get MC = MR for any of the three ranges? If Q is equal to 20, MC =10, MR = 100-2*20=60. If Q is less than 20, MR is even bigger. If Q is equal to 50, MC = 8, MR = 100-2*50=0. So MC and MR must cross somewhere between 20 and 50. Setting MC = MR  100-2Q=8  Q=46, P=54, Profits=54*46-(100+10*20+8*26)=1976

17. September 19, 2009Section 4 Section Notes17 C) We want MC = MR since we’re a monopoly. TC = 100 + Q 2  MC = 2Q TR = P(Q)*Q = (20-Q)*Q  MR = 20 - 2Q MC = MR  2Q=20-2Q  4Q=20  Q=5 P=15, Profits = TR – TC = 15*5 – 125 = -50  Shut down. You’ve done all you possibly can to maximize profits (MC = MR) and you still lose money.

18. September 19, 2009Section 4 Section Notes18 Real world: A lot of firms don’t decide how to pick Q based on carefully comparing MC to P or MC to MR. Why? Why should we not worry?

19. September 19, 2009Section 4 Section Notes19 Extra Problem Given a cost function: C(Q)=10+2Q+0.5Q 2 What are the fixed costs? What are ATC, AVC, MC? At what Q is ATC is minimized? Does this function exhibit economies of scale?

20. September 19, 2009Section 4 Section Notes20 Extra Problem Given a cost function: C(Q)=10+2Q+0.5Q 2 What are the fixed costs? What are ATC, AVC, MC? Fixed costs are 10. ATC=C(Q)/Q=10/Q+2+0.5Q AVC=VC/Q=2+0.5Q MC=dC(Q)/dQ= 2+Q

21. September 19, 2009Section 4 Section Notes21 Extra Problem Given a cost function: C(Q)=10+2Q+0.5Q 2 At what Q is ATC is minimized? From last slide: ATC=C(Q)/Q=10/Q+2+0.5Q To find where ATC is minimized, set dATC/dQ = 0 dATC/dQ= -10/Q 2 +0.5=0  Q=2√5 Alternately, recall that ATC is minimized where ATC=MC. 10/Q+2+0.5Q=2+Q  Q=2√5

22. September 19, 2009Section 4 Section Notes22 Extra Problem Given a cost function: C(Q)=10+2Q+0.5Q 2 Does this function exhibit economies of scale? Recall from lecture that economies of scale describe how the firm’s average costs change as output increases. If ATC increase with quantity, we have “diseconomies of scale”. If ATC decrease with quantity, we have “economies of scale”. Let’s check for our case: ATC=C(Q)/Q=10/Q+2+0.5Q dATC/dQ= -10/Q 2 +0.5  If we set this equal to 0, we find 20=Q 2  at Q=√20 we have a min.  For some values of Q we have “economies of scale” and for other values we have “diseconomies of scale”.

23. September 19, 2009Section 4 Section Notes23 Common Midterm Mistakes The final will be cumulative, so the material from the first part is still relevant.

24. September 19, 2009Section 4 Section Notes24 5) Please be precise and accurate. E.g. avoid “weasel words” like “may”, “might”, “could”, “likely”, “probably”, “possibly”, “potentially”… unless you really do mean that it is uncertain. E.g. if something is perfectly inelastic, it’s not just relatively inelastic – it doesn’t respond to price at all. 4) Not listing all the possible actions a risk-loving/risk-averse Martha might take. 3) Maximizing profits is not the same as maximizing revenue. We care about profits when making decisions (see question 3b in this problem set). 2) Price elasticity of durables vs. non-durables (similar to #5: be comprehensive). And, the #1 mistake… 1) Not reading the question.