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of $2,000 per week for promotional expenditures. It becomes: TC = 10,000 + 3Q + 0.0001Q2(6) Write an algebraic expression for the firm’s weekly profit function. Then find the profit maximizing level of output, Q. (Be sure to show your calculations.) (3) c. What price should the firm charge to achieve the profit maximizing level of sales? (Be sure to show your calculations.) What will the firm’s weekly profit be at this price and output level?
4 5. You have estimated a multiplicative exponential cost function for supermarkets located in metropolitan areas. The functional form is shown on the left, while the transformed function used in the estimation process is shown on the right: TC = eboQb1euln(TC) = b0+ b1ln(Q) + u where TCis weekly cost, Qis weekly sales, b0and b1are parameters to be estimated, and uis a random error term. Your regression results were: Parameter Standard t Variable Estimate Error Statistic Constant 0.336 0.163 2.061 ln(Q) 0.961 0.042 22.88 R-Squared: 0.268 σu: 0.091 The parameter estimate for ln(Q) is an estimate of the elasticity of total cost with respect to the level of output. (6) a. Use a one-tailed test with a 95% level of confidence to determine whether the elasticity of total cost with respect to the level of output is significantly less than 1.0. State your null and alternative hypotheses and show your calculations. The critical t value is 1.665. (2) b. Based on your estimation results and your hypothesis test, what can you say about economies (or diseconomies) of size in supermarket operations?
5 6. The supermarket industry has been undergoing rapid transformation in recent years. The share of the food dollar spent in supermarkets has declined quickly as food sales have increased in supercenter stores (e.g. WalMart and Target), drug stores (e.g. Walgreens and CVS), dollar stores, and convenience stores. Consumers also spend an increasing portion of food purchased on food away from home. From the point of view of a conventional supermarket chain, identify what you believe are the most important of Porter’s five competitive forces. Explain your reason for choosing each. (4) a. (4) b. 7. Centerville Power and Light (CP&L) is a small electric utility located in north central Wisconsin. CP&L currently uses a coal-fired generator to satisfy base-load electricity demand. The company currently burns both high sulfur Eastern coal (E COAL) and low sulfur Western coal (W COAL). Eastern coal is more expensive ($50 per ton), but it is also more efficient in generating the heat needed to produce electricity. Each ton of Eastern coal generates 40 million BTUs while emitting 0.025 tons of sulfur dioxide and 10 pounds of particulate emissions. Although Western coal does not generate as much heat as eastern coal (30 million BTUs per ton), it is less expensive ($25 per ton). Each ton of Western coal emits 0.015 tons of sulfur dioxide and 15 pounds of particulate emissions. In order to meet
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Spring '18
tc, linear programming model, small peas, regular peas