ECON 201, Summer 2016 July 17, 2016 Problem Set 3 1. For the following production functions: F (K, L) = 2K 1/3 L2/3 , F (K, L) = 2K + 3L and F (K, L) = min{2K, L}: (a) Draw any two isoquants. (b) Find whether they have diminishing, constant or increasing returns to labor. (c) Find whether they have diminishing, constant or increasing returns to scale. (d) Compute the marginal product of input 1 for x2 = 10 and x1 = 4 (e) Compute the marginal product of input 1 for x2 = 10 and x1 = 6 (f) Now assume that the price per capital is r and the price per labour is w. Calculate the long-run cost functions for each production function. Find also the average and marginal costs. √ 2. A firm has a production function f (x1 , x2 ) = x1 x2 . Prices are as follows: p = 5 for the output, and w1 = 1 and w2 = 2 for the inputs. The amount of input 2 is fixed at x2 = 4 and can not be changed. (a) Compute the profit maximizing choice of inputs and output. (b) Compute profits. 3. Consider a firm with the same production function of question 2. Suppose that the firm wants to produce 40 units of output. If w1 = 40 and w2 = 10, what is the cost minimizing input levels that will produce these 40 units? 1 4. All tobacco producers in Indonesia have the following cost function (both in the short-run and in the long-run): C(x) = 8 + (1/8)x2 when x > 0, and C(0) = 0. Assume that there is pure competition and the demand function for tobacco is D(p) = 72 − 16p, where p denotes the price of tobacco. (a) Find the industry’s short-run supply function if there are four firms. (b) Find the long-run competitive equilibrium price, per firm output, industry output, and number of firms. 5. Find under which conditions, i.e. for what values of a, b and c the following production functions exhibit increasing,constant and decreasing returns to scale, where a, b and c > 0. (a) F (K, L) = cK a Lb (b) F (K, L) = min{aK, bL} (c) F (K, L) = c(aK + bL) 6. Solve 22.2 and 23.8 in Workouts in Intermediate Microeconomics. 2