Inputs are used in fixed proportions of five units of L and 4
units of K. So, the production function can be written as:
q = min{4L, 5K}
So, q = 4L = 5K
So, L = q/4 and K = q/5
Cost, C = wL + rK = [w(q/4)] + [r(q/5)] = 0.25wq + 0.2rq =
(0.25w + 0.2r)q
So, C(q) = (0.25w + 0.2r)q
What is the long-run cost function for a fixed-proportions production function when it takes five units...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...
Consider a production function of three inputs, labor, capital, and materials, given by Q= LKM. The marginal products associated with this production function are as follows: MPL = KM, MPk = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials. (a) Suppose that the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q....
for a production function q = 3L + 5K, what's the long run labor demand, long run capital demand, and long run total cost in terms of q, w, r? I need a step by step defination. I got w/r = 3/5 and I'm stuck.
7. Assume that the long-run production function can be expressed as Q-SKL? Where Q is quantity of output, K is the quantity of capital and L is the quantity of labor. If capital is fixed at 10 units in the short run then the short-run production function is: Q=10KL b. Q=50KL? Q=10L? d. 0=50L Q=500KL 8. For a linear total cost function: a. MC will be downward sloping b. MC = AVC c. AVC is upward sloping and linear d....
Question 4 a) For the production function f(L,K)= L13K2/3, find the long run cost function, marginal cost function and average cost function. (20 points) b) For the same production function above, find the short run variable cost function and total cost function when capital is fixed at 500 units. (10 Points) Question 5 Suppose inputs can be perfectly substituted at a constant rate of two units of labor for every one unit of capital, while producing the same level of...
1. A firm operates in the long run. Its long-run production function is given as: Q = LK, where Qis units of output, Lis units of labor, and K is units of capital. (a) Obtain six integer combinations of Land K when Q = 12. (b) Obtain six integer combinations of Land K when Q = 18. (c) Use the twelve integer combinations of Land K obtained in parts (a) and (b) to construct two isoquants on a two-dimensional plane....
Suppose labor (L) and capital (K) are fixed proportion inputs, and that each unit of output must be produced with exactly 5 units of labor and 2 unit of capital. The price of a unit of labor is w, and the price of a unit of capital is r. a. Write down the production function. b. Derive the equation for the expansion path. c. Derive the equation for the long-run total cost function. d. Graphically depict the labor demand curve....
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
Part I: Long-Run Production and Cost Functions (12 points) Suppose the production function of a firm is given by q Lo.5 K0,5. The prices of labor and capital are given by w 2 and r 5, respectively. a) Write the firm's cost minimization problem formally. b) What returns to scale does the production function exhibit? Why? c) What is the optimal capital to labor ratio? Show your work. d) What is the slope of the expansion path and what is...
The production function for widgets takes the following form: q = 4L + 6K a. What is the least cost combination of L and K that the firm should employ to produce 48 widgets when w = 2 and r = 4. b. Suppose the price of labor increases to w = 4 but the rental rate of capital is unchanged. If the firm still wants to produce 48 widgets at the lowest cost possible, should it alter its input...