8. For the following cost functions derive the corresponding profit functions and production functions. 1/2 1/2,1/2
5. Prove that the following function is a cost function and derive a possible production 1/2,1/2 function. C(M, r, q) = q(w+1/21.12 +1.)
(2) Consider the following production function: f(k.) 10k. k+ (a) Derive the conditional input demand functions. (b) Derive the long-run total cost, marginal cost and average cost functions. (c) State and verify Shephard's lemma for the functions derived in (a) and (b). (d) When wx = 4 and we = 1, plot the long-run total cost, average cost and marginal cost functions.
Stolper-Samuelson Suppose that the economy produces two goods, 1 and 2 and that the production functions of sector 1 and 2 are respectively given by Q = K^0.3L^0.7 and Q = K^0.6L^0.4. Answer the following questions. (a) Determine which of the goods is capital intensive. (b) Derive the corresponding unit cost functions. (c) If the prices of goods 1 and 2 are 1 and 1, make use of the unit cost functions to derive the wage and rental rates, assuming...
Labor Economics 1. Derive the labor demand functions that are associated with the two production functions given below. The level of output is denoted by q. The two inputs are labor (h) and capital (k). You should derive the function that relates the level of labor utilized at each possible output level, q 〉 0, We will assume that the price per unit of capital is r 1, that the wage rate is w 2 1. q- min[2h, 3k) 2....
The graphs of the revenue and cost functions for the production and sale of z units are shown below. The cost function is the straight line, and the revenue function is the curve. 77000 70000 63000 56000 49000 42000 35000 28000 21000 14000 0 0 100200 300 400 500 600 700 800 900 1000 1100 1200 a. Use the graph to estimate the production level z that maximizes profit. Use only values that appear on the horizontal axis for your...
These functions are eigenfunctions corresponding to the operator d^2/dx^2 What is the eigenvalue corresponding to 1. sin(2pix/a) wave functions
a) What is the market price? p = 8 b) Derive the average variable cost, average total cost, and marginal cost function. avc = 1 + q atc = 4/q + 1 + q mc = 1 + 2q c) In the short run, how much does each firm produce? qs = 6 d) In the short run, how much economic profit or loss will be obtained? ep = 2 e) Based on the results in...
Let the production function be Q = (K0.5 +L0.5)2 and assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) Find the amount of K and L necessary to produce Q = 200 when v = 8 and w = 2. (d) For general w, v and Q, find the average...
1) (Cost functions) a) Consider total cost function: C(q) = 48 + 3q2 + 2q, derive the average cost function, the marginal cost function, and the minimum efficient scale, and carefully graph the average cost and marginal cost curves. b) Consider total cost function: C(q) = 20 + 5q, derive the average cost function, the marginal cost function. How does the marginal cost compare to the average cost? Graph these two functions. Does the average cost obtain a minimum at...
Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y The input prices are w and w2 respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) 1/3 1/3 (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w, and output price...