For your convenience there is a worksheet at the end of this test. This test has a total of 15 pages. Good luck!

Transcription

1 University of Toronto, Department of Economics, ECO 204, Ajaz Hussain Test 3 Solutions Please write your name as it appears in ROSI: PLEASE FILL OUT THE INFORMATION BELOW LAST NAME: FIRST NAME: MIDDLE NAME: UT ID #: SIGNATURE: PLEASE CIRCLE THE SECTION YOU RE REGISTERED IN (NOT THE SECTION YOU RE ATTENDING) M 12 2 M 4 6 T 12 2 T 4 6 W 6 8 PLEASE CIRCLE YOUR EXAM ROOM: EX 100 EX 310 EX 320 SCORES Question Points Score Total 100 For your convenience there is a worksheet at the end of this test. This test has a total of 15 pages. Good luck! 1

2 Question 1 (This question is based on Lecture 12, Practice problems 12 and solutions, HW 10 and HW 10 Solutions). Kimonda Inc. manufactures semiconductors in a perfectly competitive industry. Currently, the market price of semiconductors is $40. Using techniques similar to the Prestige Telephone Company case, Kimonda s accountants estimate the cost function to be C = q + q 2. (a) (5 points) Assuming Kimonda produces output to maximize profits. Derive Kimonda s supply curve. Any profit maximizing firm produces where MR = MC. Now: MC = dc/dq MC = 4 + 2q In perfect competition, the demand curve is flat (slope = 0) and equal to the market price. Since the MR curve has the same intercept and twice the slope, the MR is also equal to the market price. That is: MR = P Setting MR = MC: P = MC P = 4 + 2q As written, this is not the supply curve because in this equation q is given (exogenous) and which yields price. In fact, the supply curve only exists for price taking firms, so we should have price on the right hand side and q on the left hand side: q = (P 4)/2 (b) (5 points) Based on your answer in part (a), what is Kimonda s profit maximizing output? 2

3 Currently, P = $40. Hence, from the supply curve: q = (40 4)/2 q = 18 (c) (5 points) Calculate Kimonda s profits. = R C = Pq { q + q 2 } = (40)(18) 100 4(18) (18) 2 = 224 (d) (5 points) If all incumbent and potential entrant firms in the semiconductor industry are identical to Kimonda, predict how the industry will evolve in the long run will existing firms exit or will new firms enter? Calculate the long run price. From part (c), observe that all incumbent firms are profitable; as such, new firms will enter the industry until the profits are competed away. In fact, entry will cease when firms no longer make positive profits, which happens when P = min AC. Now: C = q + q 2 AC = C/q AC = { q + q 2 }/q AC = 100/q q AC is minimized when dac/dq = 0: 3

4 dac/dq = 100/q = 0 q = 10 At this output, AC is minimized and equal to the long run price: P = min AC P = 100/ = $24 The long run equilibrium price will be $24. Our prediction is that firms will enter the industry and drive prices down from $40 to $24. (e) (5 points) Assume the semiconductor is currently in long run equilibrium. Suppose the industry has a positive demand shock. If the semiconductor industry is an increasing cost industry, predict whether the new long run price will be greater than, less than or equal to the long run equilibrium price in part (d). Draw a graph to illustrate your answer and give a short explanation for why an industry can be an increasing cost industry. Note: you re being asked to give a qualitative answer. With a positive demand shock, market demand shifts out to the right, causing the market price and output to rise 1. The higher demand for and supply of output requires more inputs. In an increasing cost industry, K and L are scarce, so that increased demand for K and L leads to higher input prices (P L and P K ). With greater demand for output and therefore greater derived demand for inputs the AC for all firms new and old rises, resulting in permanently higher long run prices. Thus, we would predict the new long run equilibrium price to greater than $24. This is depicted in Figure 1 below (reproduced from lecture 12). This question emphasizes the importance of understanding the market structure of inputs for the analysis of competitive industries such as commodities. Without an understanding of the market for inputs, it s hard to predict what will happen to the long run equilibrium price. 1 We know that both price and output must rise because the market supply curve is upward sloping (neither vertical nor horizontal). This is because in perfect competition, the market supply curve is the sum of firm supply curves which in turn from part (a) is upward sloping. 4

5 Figure 1 Question 2 Ajax Foam is the only manufacturer of fire retardant foam in Toronto. It estimates the (monthly) demand equation for its product to be: P = 1, Q and its (monthly) cost equation to be: C = 1,400, Q Q 2. Ajax Foam has a (monthly) capacity of 10,000 units. (a) (5 points) Solve for the (monthly) profit maximizing output using d /dq = 0. Since the decision variable is Q, express profits as a function of Q: (Q) = R(Q) C(Q) (Q) = P(Q)Q C(Q) (Q) = ( Q)Q {1,400, Q Q 2 } (Q) = 1500Q 0.1Q 2 1,400, Q 0.05Q 2 5

6 d (Q)/dQ = Q Q = Q = 0 Q = 1200/0.3 Q = 4,000 Since this is below the capacity of 10,000, this output is feasible. (b) (5 points) Solve for the optimal output using MR = MC MR = MC 1, Q = Q 1,200 = 0.3Q Q = 4,000 which is the same answer we got in part (a). (c) (5 points) A manager at Ajax Foam armed with a MBA from UBC (University of Bad Characters) argues that by producing the output in parts (a) and (b) the company is wasting capacity. Prove this manager wrong. Show all calculations. We did a similar question in HW 11. From part (a): (Q) = 1500Q 0.1Q 2 1,400, Q 0.05Q 2 (Q) = 1200Q 0.15Q 2 1,400,000 Now, profits at the optimal output of Q = 4,000: (4,000) = 1200(4,000) 0.15(4,000) 2 1,400,000 = $1,000,000 or $1m 6

7 Now, profits at the capacity output of Q = 10,000: (10,000) = 1200(10,000) 0.15(10,000) 2 1,400,000 = $4,400,000 or a loss of $(4.4)m Thus, the MBA from UBC is incorrect: given current demand and cost conditions, it is optimal to produce below capacity. (Review HW 11 again). (d) (5 points) Suppose the Government of Ontario decides to regulate Ajax Foam to force it to behave as if it s a competitive firm. Solve for the regulation price and output. Draw the regulated monopoly demand, MR, MC, output and price below and write down the equations for regulated demand and MR. If the government wishes Ajax to behave as a competitive firm, it should impose a price ceiling at the price corresponding to the output where P = MC. Using the expression for demand and MC from above: P = MC 1, Q = Q 1,200 = 0.2Q Q = 6,000. This answer is feasible since it is below the capacity of 10,000. Hence, the regulation price is: P = (6000) = $900. This is depicted in Figure 2 below: 7

8 Figure 2 The equations for the regulated demand and MR are: P = $900 for q = [0,6000] and P = 1, Q for q > 6000 MR = $900 for q = [0,6000] and MR = 1, Q for q > 6000 Question 3 You re responsible for setting prices at a concert hall with a seating capacity of 36,000. For this problem, assume MC = 0 (i.e. it costs you nothing to serve concert goers). (a) (5 points) Superstar Bad donna will be performing at your concert hall next week. Demand for her concert is estimated to be Q = 60,000 3,000P. What is the optimal price? Hint: What is your objective? Be careful using the shortcut for MR. Since MC = 0, maximizing profits using MR = MC is equivalent to maximizing revenues (MR = 0) (see HW 11 for example). Now, for a linear demand curve, MR has the same intercept and twice the slope of the demand curve as long as P is on the left hand side (see Lecture 13 slide 18). Hence: 8

9 Q = 60,000 3,000P P = 20 (1/3,000)Q MR = 20 (1/1,500)Q Setting MR = 0 yields: MR = 20 (1/1,500)Q = 0 Q = 30,000 This is well below the capacity and is a feasible answer. At this demand, price will be: P = 20 (1/3,000)Q P = 20 (1/3,000)(30,000) = $10 Thus, you will price tickets at $10 and will attract 30,000 concert goers for the Bad donna concert. (b) (5 points) What is the price elasticity for your answer in part (a)? Hint: The formula for price elasticity is E = (dq/dp)(p/q). Actually, you can do this question without computing E. Your objective in part (a) is to maximize revenues. Since you have a linear demand curve, revenue maximization occurs where E = 1. If you want, you can show this by computing E: E = (dq/dp)(p/q) E = 3,000(10/30,000) = 1. E = 1 9

10 (c) (5 points) Next month, the Canadian group Nickel Front will be performing at your concert hall. Demand for their concert is estimated to be Q = 120,000 3,000P. What is the optimal price? Hint: What is your objective? Be careful using the shortcut for MR. Since MC = 0, maximizing profits using MR = MC is equivalent to maximizing revenues (MR = 0). Now, for a linear demand curve MR has the same intercept and twice the slope of the demand curve as long as P is on the left hand side (see Lecture 13 slide 18). Hence: Q = 120,000 3,000P P = 40 (1/3,000)Q MR = 40 (1/1,500)Q Setting MR = 0 yields: MR = 40 (1/1,500)Q = 0 Q = 60,000 This is above the capacity of 36,000 and is not a feasible answer. Thus, you will price tickets to fill 36,000 concert goers. At Q = 36,000, the price should be: P = 40 (1/3,000)Q P = 40 (1/3,000)(36,000) = $28 Thus, you will price tickets at $28 and will attract 36,000 concert goers for the Nickel Front concert. Question 4 (This question is based on Lecture 16). Burger Queen (BQ) sells the Slopper (a burger made of mystery meat) through independently owned franchise restaurants. BQ sells ingredients for the Slopper at cost to franchise restaurants. Suppose the MC of ingredients is $1. Under the terms of the current contract, BQ takes 25% of every franchise s revenues and BQ sets the price. 10

11 (a) (5 points) Daily demand for a franchise in North York with a daily capacity of 600 sloppers is estimated to be P = 6 Q/200. Calculate the optimal price and daily sales of sloppers for this location. Show all calculations. BQ s objective is to maximize 0.25 R which is the same as maximizing R. Hence, it will choose an output where MR = 0. Now: P = 6 Q/200 MR = 6 Q/100 MR = 0 yields: MR = 6 Q/100 = 0 Q = 600 Note how the optimal Q is feasible since it equals capacity. Thus: P = 6 Q/200 = 6 600/200 = $3. BQ will set a price of $3 per slopper and will sell 600 sloppers a day in the North York location. (b) (5 points) Suppose the BQ shares a percentage of total profits with the North York franchise. Calculate the optimal price and daily sales of sloppers. Show all calculations. Both parties regardless of their share of profits will seek to maximize profits. Thus, the rule will be MR = MC. Now: P = 6 Q/200 MR = 6 Q/100 11

12 MR = MC yields: MR = 6 Q/100 = 1 Q = 500 Note how the optimal Q is feasible because it s capacity. Thus: P = 6 Q/200 = 6 500/200 = $3.50 With profit maximization, the price of a slopper is $3.50 and sales are expected to 500 sloppers a day in the North York location. (c) (5 points) Daily demand for a franchise in Mississauga with a capacity of 500 sloppers/day is estimated to be P = 6 Q/200. Calculate the optimal price and daily sales of sloppers for this location under the contract where BQ takes 25% of the franchisee s revenues. Show all calculations. Note how the Mississauga location has the same demand as the North York location albeit with a lower capacity. In part (a), the optimal output was 600 sloppers. Hence, without doing the question, you can tell that the optimal answer for Mississauga also has to be 600 sloppers, which is not feasible since the restaurant has a capacity of 500 sloppers. Thus, the optimal output has to be 500 sloppers. If you want to show this the long way here it is: BQ s objective is to maximize 0.25 R which is the same as maximizing R. Hence, it will choose an output where MR = 0. Now: P = 6 Q/200 MR = 6 Q/100 MR = 0 yields: MR = 6 Q/100 = 0 Q =

13 Note how the optimal Q is infeasible since it s above capacity. Thus: P = 6 Q/200 = 6 500/200 = $3.50. BQ will set a price of $3.50 per slopper and will expect to sell 500 sloppers a day in the Mississauga location. Observe how this is the same answer as the case of profit sharing with the North York franchise. This shows that just because various franchisees charge the same price does not mean they have the same contract. Question 5 Spurred by the success of major sports leagues such as the NBA, NHL, NFL and UFC you start a new sports league BED: Battle of Economists unto Death. This profit maximizing league organizes gladiator style fights between prominent economists. BED s costs stem from printing tickets only. Suppose Q is measured in thousands. A typical match hall has a capacity of 2,000 or Q = 2. (a) (5 points) In March 2009, Professor Pea sando will battle Lord Maynard Keynes. Suppose demand for March 2009 is estimated to be P = 25 5Q and MC is estimated to be MC = 5. How many tickets will you print and sell? At what price? BED wishes to maximize profits. It sets MR = MC: 25 10Q = 5 Q = 20/10 = 2 This answer is feasible: therefore, you will print and sell 2,000 tickets at a price of: P = 25 5(2) = $15 (b) (5 points) In April 2009, Professor Hussain will battle Eco man. Suppose demand for April 2009 is estimated to be P = 25 5Q and MC is estimated to be MC = 5. However, before any tickets are printed, the MC estimate changes to MC = 10. How many tickets should you print and sell? At what price? BED wishes to maximize profits. It sets MR = MC. Since MC has been revised before printing (i.e. 13

14 production), we simply re compute MR = MC using the new MC: 25 10Q = 10 Q = 15/10 = 1.5 This answer is feasible. Therefore, we will print and sell 1,500 tickets at a price of: P = 25 5(1.5) = $17.5 (c) (5 points) In May 2009, Professor G Indart will battle Milton Friedman. Suppose demand for May 2009 is estimated to be P = 25 5Q and MC is estimated to be MC = 5. However, after all tickets are printed, the demand forecast is revised to P = 10 Q. How many tickets should you sell? What is the price of the tickets? BED wishes to maximize profits. With the initial demand and cost forecasts, BED will print tickets by setting MR = MC: 25 10Q = 5 Q = 20/10 = 2 Or 2,000 tickets. In light of new demand information, BED sets MR = MC but uses MR from the new demand curve and since demand has been revised after printing (i.e. production) uses MC = 0 as all printing costs have been incurred and are sunk. 10 2Q = 0 Q = 5 However, this exceeds the number of tickets already printed. Thus, BED will sell Q = 2 or 2,000 tickets at a price of: P = 10 2 = $8 Question 6 (5 points) In the DeBeers case, we discussed why the CSO has a take it or leave it deal with sight holders. Briefly explain why DeBeers does this does this offer any insights for business transactions? 14

15 Answer Diamonds are not a commodity. Unlike homogeneous, undifferentiated goods, there are enormous variations in diamonds even within a C (cut, clarity, color) category. If sight holders are allowed to cherry pick, the transaction will take an inordinately long time, raising the cost of doing business to both the CSO and the sight holders. The solution is to have the CSO a monopoly restrict cherry picking. As we discussed in class, there are lessons for business. Whenever there is heterogeneity in goods, it s good to restrict cherry picking in order to lower the cost of doing business. This is why fruit sellers stop you from picking through fruits. Question 7 (5 points) Briefly explain how product proliferation can be an endogenous barrier to entry. Consumers have preferences over attributes of goods and services. For example, consumers may care about sweetness and crunchiness in cereals, or, horsepower and manual transmission in cars. If a company proliferates products in an attribute space, it leaves no empty attribute space for a new comer to exploit. Without a fallow spot, new firms don t enter. Hence, product proliferation acts as an endogenous barrier to entry. See lecture