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Unformatted text preview: Economics 3070 Fall 2008 Problem Set 1 (Due Sept. 10 th in class) Chapter problems are from edition 2 of the textbook 1. Ch 1, Problem 1.3 A firm produces cellular telephone service using equipment and labor. When it uses E machine-hours of equipment and hires L person-hours of labor, it can provide up to Q units of telephone service. The relationship between Q , E , and L is as follows: EL Q = . The firm must always pay P E for each machine-hour of equipment it uses and P L for each person-hour of labor it hires. Suppose the production manager is told to produce Q = 200 units of telephone service and that she wants to choose E and L to minimize costs while achieving that production target. a. What is the objective function for this problem? The objective function is the relationship the production manager seeks to maximize or minimize. In this example, the production manager wants to minimize costs. The production manager’s costs are given by the following expression: P E E + P L L . Thus, the objective function is: min P E E + P L L . b. What is the constraint? The constraint will describe the restriction imposed on the production manager. Since the production manager is told to produce Q = 200 units of telephone service, the constraint is 200 = EL . c. Which of the variables ( Q , E , L , P E , P L ) are exogenous? Which are endogenous? Explain. The exogenous variables are the ones the production manager takes as given when she makes her decisions. Since she takes the production target ( Q = 200) as given, Q is exogenous. The prices of equipment ( P E ) and labor ( P L ) are also exogenous, since she cannot control these prices. The production manager’s only choices are the number of machine-hours of equipment ( E ) to use and the number of person-hours of labor ( L ) to hire. Therefore, E and L are the endogenous variables. Economics 3070 Fall 2008 d. Write a statement of the constrained optimization problem. The statement of the constrained optimization problem is ( ) L P E P L E L E + , min subject to: 200 = EL The first line shows that the production manager wants to choose E and L to minimize costs. The second line describes the constraint: the production manager must produce 200 units of telephone service. 2. Ch 1, Problem 1.9 A major automobile manufacturer is considering how to allocate a $2 million advertising budget between two types of television programs: NFL football games and PGA tour professional golf tournaments. The table below shows the new sports utility vehicles (SUVs) that are sold when a given amount of money is spent on advertising during an NFL football game and a PGA tour golf event. New SUV Sales Generated (thousands of vehicles per year) Total Spent (millions) NFL Football PGA Tour Golf $0 0 0 $0.5 10 4 $1.0 15 6 $1.5 19 8 $2.0 20 9 The manufacturer’s goal is to allocate its $2 million advertising budget to maximize the number of SUVs sold. Let F be the amount of money devoted to advertising on NFL football games,...
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This note was uploaded on 09/12/2009 for the course ECON 3070 taught by Professor Raisenen during the Fall '09 term at University of Colombo.
- Fall '09