MBA 201A—Economic Analysis for Business DecisionsANSWERS - Problem Set #4UNIVERSITY OF CALIFORNIAHAAS SCHOOL OF BUSINESSMBA 201A—Economic Analysis for Business DecisionsFall 2009 Professor Catherine WolframANSWERS - Problem Set #4Question 1You have just inherited a piece of property that has two functioning oil wells on it. The inheritance is unusual in that you only are allowed to keep the land for 1 year. After that, you must turn it over to your evil twin brother, who is less deserving than you. Each oil well requires a separate operator, which costs 2,500 per month per operator. Assume that you can hire operators on a month-to-month basis. Well 1 is the more efficient one. The cost of extracting B barrels of oil in a month is TC1=2500 + 0.05 B2 (the 2500 reflects the monthly operator cost). If you shut the well down, it costs you zero. The cost of extracting B barrels of oil in a month from well 2 is TC2=2500 + 0.1 B2. If you shut the well down, it costs you zero. The operators are hired on a month-to-month basis, so you can lay them off during the year and stop paying their salaries.a) If the price at which you could sell the oil were 30/barrel, would you operate well1? If so, how much would you produce each month? How much profit would you make? Would you operate well 2? If so, how much would you produce each month? How much profit would you make?From the total cost functions, we can calculate that MC1=0.1B, so setting MC1=P → B1=300 → Profit1 =TR-TC=9000-(2500+0.05(3002))=2000. You can make 2000 per month, or 24,000 for the year, operating well 1. Likewise, MC2=0.2B, so setting MC2=P→ B2=150 → Profit2=TR-TC=4500-(2500+0.1(1502))=-250. If you operate well 2 when the price of oil is 30/barrel, the best you can do is lose 250 per month. Shut down well 2.b) Instead of the price being 30/barrel all year, it instead turns out to be 35 in the first six months of the year and 25 in the last six months of the year. How much do you produce from each well during each month? Are your profits for the yearhigher or lower than in part a? Explain this outcome.When the price of oil is 25, MC1=P→B1=250 → Profit1=TR-TC=6250-(2500+0.05(2502))=625. When the price of oil is 35, MC1=P → B1=350 → Profit1=TR-TC=12250-(2500+0.05(3502))=3625.If the price of oil is 25 for six months of the year and 35 for the other six months,then total profit for the year from well 1 is 6x625 + 6x3625 = 25500.MBA 201a Fall 2009—Prof. WolframWhen the price of oil is 25, MC2=P→ B2=125 → Profit2=TR-TC=3125-(2500+0.1(1252))=-937.5, so don't operate the well.When the price of oil is 35, MC2=P → B2=175 → Profit2=TR-TC=6125-(2500+0.1(1752))=562.5. If the price of oil is 25 for six months of the year and 35 for the other six months,then total profit for the year from well 2 is 6x0 + 6x562.5 = 3375.Your profits are higher when the price fluctuates over time (but has the same average as before). This is because you have the option of not producing the same amount all the time. By producing more when the price is high and less when it is low, you increase profits.c) What is the average cost function for operating well 1? For operating well 2?AC1=TC1/B=2500/B+0.05B. AC2=2500/B+0.1B.d) At what price of oil would you shut down well 1? At what price would you shut down well 2? How do these prices relate to the average cost functions you identified in part c? You would shut down well 1 if the price were so low that even when you did your best to maximize profits, the result was negative profits. One way to figurethis out is to look at the average cost function. So long as the price is higher than some point on the average cost function, you can make positive profits by producing a quantity for which P>AC, because P>AC → PxB > ACxB → TR>TC → Profits>0. If price falls below the minimum AC value, then there is no quantity at which you can make profits. You can find the minimum AC by finding where MC=AC. For well 1, MC1=AC1 → 0.1B = 2500/B+0.05B → 0.05B2=2500 → B=223.6 → AC=22.3. If the price falls below 22.30, shut down well 1. Likewise, MC2=AC2 → 0.2B = 2500/B+0.1B → 0.1B2=2500 → B=158.11 → AC=31.62. If the price falls below 31.62, shut down well 2.2MBA 201a Fall 2009—Prof. WolframQuestion 2The market for pencils is easy to enter, but entry takes time. In the short run, the number of firms (and plants) in the industry is fixed. Production occurs in standard sized plants with each plant having an annual total cost function of TC=400+q2 (this includes a normal return on the plant's capital). This, of course, means that each plants’ marginal cost of production is MC=2q and its average cost of production is AC=400/q + q. Currently, no firm owns more than one plant. Pencils are a completely homogeneous good.a) You own one plant among more than a hundred in the industry. Currently, the price of a pencil is P=100. How many pencils do you produce each year? What are your annual profits?Since pencils are a completely homogeneous good and you are a small part of the plant, you are a price-taking firm. So, you take the market price as given, P=100. Likeall firms, you maximize profits by producing so long as MR>MC, but since you are a price-taking firm, MR is just the market price, P. You continue to increase production, so long as MC<P, so you produce until MC=P → 2q=100 → q=50. Your profits are Profit=TR-TC=100x50 - (400+502)=2100.b) The demand in the market is Q=50,000-200 P. As stated in (a), the price is P=100. If the market is in short-run equilibrium (meaning each firm is maximizing its profits given that the number of plants is fixed in the short run), how many firms are in the market?If P=100, then each firm must be producing q=50. For the industry to fulfill the demand at P=100, it must produce Q=30000. Thus, there must be 30000/ 50=600 firms in the industry.c) Explain why this market is not in long-run equilibrium. Derive the long-run equilibrium in this market. What is the equilibrium price? What is the equilibrium quantity sold by each firm? How many firms are in the market?This market is not in long run equilibrium, because new firms can easily enter and, at the current market price of P=100, make positive economic profits. In the long run, wewould expect new firms to enter. In long run equilibrium, each firm must be maximizing its short run profits (MC=P) and additional firms cannot earn economic profits by