Homework 2: Managerial Economics Due Date: September 13, 2018

Transcription

1 Homework 2: Managerial Economics Due Date: September 13, 2018 uestion 1 a. For = 8 we can compute the total fixed costs. We have: TC = TFC +TVC, (1) TC = TFC + AVC, (2) 1070 = TFC +8 15, TFC = 350. (3) The total fixed costs do not change with the quantity; they are the same for all values of. Next, we can compute average variable costs for the remaining quantities. For = 18, I get: AVC = TVC = TC TFC = =.61. () For average total costs when = 18: ATC = TC = = (5) For marginal costs we need only total costs and. For = 21: MC 21 = = 11. (6) For problem (d), we will also need the profits. For = 18 given that the price is $22, I get: π 18 = P TC = = $37. (7) The rest of the numbers are in the table. 1

2 Production () Total costs Total Fixed Average Variable Average Total Marginal NA Profit Table 1: Average and marginal costs: Artisanal Bologna Company. b. To maximizeprofits, weset priceequal tomarginalcost. Thepriceis$22, andmarginal costs are $22 at approximately 3-36 units (highlighted in blue in the table). c. Average profits are: π = TR TC, (8) = P ATC = P ATC. (9) The price is constant so average revenues are always P = $22. Therefore, to maximize average profits, we need to make the second term in equation (9), average total costs, as small as possible. On the table, average total costs are smallest at about 32 units (highlighted in red). d. Units between 32 and 3 make profits for the firm, since P > MC for these units. They make less profits than the previous units, thus causing average profits to fall. Nonetheless, they still add to profits and therefore should be produced. e. Since average variable costs in the table are not constant, we must calculate profits directly. These are calculated in the last column of table 1, using π = TR TC. The break even point is between 21 and 2 units. At this point, we have paid off the fixed costs. There is second point with zero profits at -8 units. At this point, production 2

3 is so high that diminishing marginal product has set in and workers are so numerous and unproductive that profits drop to zero. However, this is not a break even point, but instead just illustrates that if we produce too much profits can be negative. uestion 2 a. Long run average costs are u-shaped. By increasing output(number of screens), average cost per screen falls. The fixed cost of the single restroom, lobby, ticket seller, and projection and concession operators are spread across more screens. So average costs fall with the number of screens initially. However, if the number of screens is large enough, the theater faces additional costs to relieve congestion. For example, larger lobbies and parking lots. Thus average costs start to rise when the number of screens is large. b. Indivisibilities is a clear reason for decreasing long run average costs. When screens are added, additional labor is not needed. So there must not have been enough work to fully utilize each type of worker. One could similarly argue that the restroom and lobby also have indivisibilities. One could also argue engineering reasons for decreasing long run average costs. It is cheaper per screen to build a theater with many screens versus a smaller theater. uestion 3 a. Long run average costs are decreasing. As stated in the quote, as firms in the industry get bigger, they get better pricing from suppliers, which decreases their long run average costs. b. Since long run average costs are decreasing, Sears should get bigger, not smaller. However, as stated in class, this is easier said than done. First, the demand is not there, and installing more stores is unlikely to generate much more demand. Second, the company has negative cash flows, so obtaining financing for an expansion would be difficult. Third, the company needed to sell assets to stave off bankruptcy. However, this creates the death spiral. By selling off assets, the company gets worse deals from suppliers and long run average costs rise. Sears will then lose even more money in the future and will have to sell off still more assets. The correct strategy is to sell the entire firm (or liquidate assets). Only by merging with a larger competitor can Sears hope to remain competitive. Indeed, two weeks after this article, an analyst came out recommending exactly this strategy. uestion (requires Tuesday s notes) 3

4 a. To minimize long run average costs, we set the derivative equal to zero: dlrac d = = 0, = 650. (10) Long run average costs are minimized for a hospital system with 650 beds. b. In the long run competitive equilibrium, economic profits are zero (if positive, then the industry would see entrants and pricing power). P = LRAC = , (11) P = LRAC = , P = $2000. (12) The long run equilibrium price is $2,000 per bed. c. We have: π = P TC = P LRAC. (13) π = 2000 ( ) = $7,2. (1) UM is losing $7,2 per bed. Although UM earns $2,000 in revenue per bed, its costs are just too high because it has not taken advantage of scale economies that occur in a larger hospital. These include better deals from suppliers and indivisibilities such as billing. d. UM needs to merge with a larger hospital system. The ideal size is 650 beds, so UM needs to merge with a hospital that has = 610 beds. Although these numbers are not real, the problem and solution are: university hospitals across the country are merging with larger hospital systems to take advantage of scale economies and improve their pricing power with insurers. uestion 5 (Requires Tuesday s notes) a. We can use the percent change formula for elasticity: e P = % Change in % Change in P, (15)

5 e P = 20% 17% = (16) For a 1% increase in the price, the quantity of Iphones sold falls by 1.176%. b. Demand is elastic. A 1% increase in the price generates a more than 1% decrease in the quantity of Iphones sold. c. We can look at this problem from the revenue side. The price previous to the revenue increase is: % = P new P old P old, (17) 0.17 = $767 P old P old, (18).17P old = $767 P old, P old = $ (19) So total revenues before the price increase are: TR old = P old old = $ M = $3,266.96M = $3.267B. (20) Total revenues after the price increase are: TR new = P new new = $767 53M = $0,651M = $0.651B. (21) Whew, Apple has a lot of revenue. But revenue went down. This is true generally, when the price elasticity is in the elastic range, increasing the price will result in less revenue. HOWEVER, we will see later that the firm may still want to do this. Apple also saves on costs because it has to make 13 million less Iphones. So total profits may go up. To find out, we would need the cost data as well. uestion 6 a. If demand is MW, we need either 2 107m diameter windmills, or one 150m, or one 16m, or one 220m. Hereafter I will call them small, medium, large, and extra large. Average costs are: ATC = AFC +AVC, (22) 5

6 ATC = TFC Thus for the two small windmills, ATC 107 = $5,00,000 2 For the other windmills: ATC 150 = $6,000,000 +AVC. (23) +($ $ $0.6 + $0.23) = $2,700,00.57/MW,(2) +($2.80+$0.60+$0.0+$0.20) = $ (25) ATC 16 = $8,550,000 +($2.72+$0.58+$0.39+$0.19) = $87.00 (26) ATC 220 = $9,600,000 For the rest of the MWs I get: +($2.56+$0.55+$0.37+$0.18) = $25.72 (27) Average Total Cost Demand Forecast LRAC $2,700,00.57 $1,500,00.00 $2,137, $2,00, $1,500, $1,800,00.57 $1,000,00.00 $1,25, $1,600, $1,000, $2,025,00.57 $1,500,00.00 $1,068, $1,200, $1,068, $1,620,00.57 $1,200,00.00 $1,710, $960, $960, $1,800,00.57 $1,000,00.00 $1,25, $800, $800, $1,52, $1,285, $1,221,32.5 $1,371,32.22 $1,221, $1,687,50.57 $1,125,00.00 $1,068, $1,200, $1,068, $1,500,00.57 $1,000,00.00 $950, $1,066, $950, $1,620,00.57 $1,200,00.00 $1,282, $960, $960, $1,718, $1,090, $1,165, $872, $872, $1,575,00.57 $1,000,00.00 $1,068, $800, $800, Table 2: Average total cost of alternative windmills. b. The LRAC is the lowest cost of production for each output level. So for demand of MW, 1 medium has the lowest cost. The point on the LRAC is (,$1,500,00). Similarly, the other points given in the last column of table 2. 6

7 c. We should get all electricity from the large windmill and leave the medium sized windmill idle, because the large windmill has lower average variable (operating) costs. The fixed costs are sunk and do not matter. This part of the question was generated by a former student, who came to me with the opposite problem: the smaller factory had lower average variable costs, so I recommended operating the small plant to capacity and producing the remainder at the large plant. d. No. Averagefixed costsgotozeroforcruise shipsandnursing homes, since wecankeep building bigger and bigger ships/homes. We need only one factory regardless of. Here as increases, we eventually exceed capacity and have to add another windmill, which drives up average fixed costs. In addition, average variable costs cannot go below the average variable costs of the largest windmill, $3.65. uestion 7 a. The choice is to build one large facility in Seattle or 2 medium sized facilities, one in Seattle and one elsewhere. The choice is not how big should Amazon get? So we are finding the cheapest plant configuration. b. Amazon chose two medium sized plants, so this configuration must be the lowest cost and therefore on the LRAC. 7