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Unformatted text preview: Problem Set 3
Econ 115a October 2, 2007 1. Define (a) Marginal Revenue Product (b) Iso-Cost Curve (c) Technological Efficiency (d) Marginal Cost 2. The firm Widgets-R-Us uses labor, L, and capital, K, to produce Widgets. The production function is Q = L K. For this production function, the marginal productivity of labor is 1 K M PL = 2 L while the marginal productivity of capital is M PK 1 L = 2 K Say that labor receives a wage rate of w and that the cost of capital is r. (a) First, assume that capital is fixed at K. Graph the marginal productivity of labor. (In this problem, your graphs should capture the general shape of the curves, but they don't need to be at all exact.) Graph the optimal "short-run" choice of labor. (b) Give a formula for the choice of labor that you just graphed (it will depend on the wage and on K.) (c) Graph how the (short-run) amount of labor will vary with the wage. 3. Say the Eli Pharmaceutical company advertises its "Study Aid" caffeine pill in both newspapers and on TV. Denote the amount of advertising in newspapers as AN and the amount on TV as AT . Say that advertising results in purchases of Study Aid according to the "production function" Q = F (AN , AT ) The price of a newspaper ad is pN and the price of a TV ad is pT . Note that we can think of the advertising amounts an "inputs" into the production of Q. 1 (a) Graph an "iso-quant" that gives the combinations of AN and AT that would produce a given quantity of sales Q. What do you give it that shape? (b) Add a set of "iso-cost" lines to your graph and show, for the given output level, the optimal (cost-minimizing) choice of the two kinds of ads. (c) In this example, what is the slope of the iso-quant? What is the slope of the iso-cost curve? (d) On a separate graph, show how (for the same Q) the cost-minimizing advertising choices would change in if the price of newspaper ads declined. 2 ...
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- Fall '07
- Economics, marginal productivity, marginal revenue product