Consider the two production functions: i Fixed proportions: q = [min (k, l)] s ii Perfect substitutes: q = (k + l) s (a) Explain why the parameter s (> 0) measures returns to scale in each of these production functions. (b) Calculate the total cost function for each of these production functions. (c) Calculate the average and marginal cost functions.
1. Suppose that a profit-maximizing firm, operating in a
F(L,K) = L^1/2 + 2(K^1/2)
where L are the units of labor and K the units of capital. Suppose further that in order to operate, the firm must pay the government a fixed value patent of $ 50, no matter how much it decides to produce. Finally, consider that the factor price is given by w = 1 and r = 4, respectively.
(a) Calculate the TMST, placing L on the x-axis. What value does the TMST take when L = 0, and what value does it take when K = 0? Explain if you can or
there are no corner solutions to the cost minimization problem.
(b) Find the conditional demands L (q) and K (q), and the cost function C (q) in the long run.
2. A company has a production function equal to f (L, K) = 2L + βK. Suppose that the firm currently achieves a level of production equal to q0, using for this a certain amount of capital and labor.
(a) If the firm wanted to decrease the amount of labor by x units and maintain its production at q0, by how much should the contracted capital increase?
(b) What value (or range of values) must β acquire for the expansion path of the firm to have a completely vertical shape?
(c) If the condition described above is fulfilled, determine the forms of the functions of the demands conditioned by capital and labor,
the least cost, marginal cost, and average cost function of
this company.
3. Consider the two production functions:
i Fixed proportions: q = [min (k, l)] s
ii Perfect substitutes: q = (k + l) s
(a) Explain why the parameter s (> 0) measures returns to scale
in each of these production functions.
(b) Calculate the total cost function for each of these production functions.
(c) Calculate the average and marginal cost functions.
3
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
