4) Jordan is producing shoes with the production function y = min {1/2x1 ,x2 , 2x3 } , where x i is a factor of production, i = 1,2, 3 . Jordan buys her inputs at constant prices: w 1 = $10 , w 2 = $14 and w 3 = $6 . Her cost function is:
Cost function is represented by production costs in terms of the amount of good produced.
TC = w1.x1 + w2.x2 + w3.x3
TC = 10x1 + 14x2 + 6x3
4) Jordan is producing shoes with the production function y = min {1/2x1 ,x2 , 2x3...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
A producer produces good y using inputs x1 and x2 according to
the production function y = xα1xβ2 where α+β < 1. The factor
prices are w1 and w2 (for input 1 and 2). The producer can sell as
much as he wants at unit price p.
A producer produces good y using inputs X1 and 22 according to the production function y = xqx, where a + B < 1. The factor prices are wi and W2 (for input...
5. Let the firm's production function be given by y = + x2. Note that the inputs 2 and 2 are perfect substitutes in this production process. Suppose w = 2 and we = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of...
3. Consider the linear production function y = axı + B.x2 where xı and X2 are inputs with prices wi and W2 respectively. (a) Derive the conditional factor demands for rı and 22. (b) Derive the cost function. (c) Derive the short-run cost function when input 2 is fixed at 72. (d) Derive both short- and long-run average cost functions.
full solutions would be
appreciated!!
9) A firm has a production function y - 3z1 +x2. If the factor prices are $12 for factor 1 and $3 for factor 2, what is the minimum cost of producing 30 units of output? a.$1,170 b. $1,080 c. $360 d. $180 e. $90 (+) 10) The production function is ???(L. K) 2L1/2K1/2, where L is the number of units of labour and K is the number of units of capital used. If the...
5. Let the firm's production function be given by y = x1 + x2. Note that the inputs 21 and 2 are perfect substitutes in this production process. Suppose w = 2 and w2 = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price...
1. Consider the following production function: Y = A min{2N, K} (1) where A measures productivity, N is labor employed by the firm, and K is capital. The firm chooses labor and capital, taking productivity as given. Labor can be purchased at a constant wage, W, and capital at a constant rate, R. (a) Derive the cost function C = C(W,R,Y) for the firm. (b) Show that costs decrease in productivity, A. (c) Consider two companies with cost functions Yị...
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production function is 1/2 1/4 = xi X2. (4) Note that (4) is a special case of the production function in Question 1, in which 1/4 1/2 and B a = Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously given factor...
Problem 1: A firm has the following production function: min{x1, 2x2) f(x,x2)= A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the optimality condition that determines the firm's optimal level of inputs? C) Suppose the firm wants to produce exactly y units and that input 1 costs $w per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? D) Using the information from part D), write...
1- Suppose that a firm producing commodity with the following production function: Y = 20X,X2 Then, assume that the maximum amount the firm can spend on these two inputs is $100 and price of commodities are as follow: Xi = 4, X2 = 5 a. Use Lagrange Multiplier to determine the optimal production level at this firm. b. What is the meaning of shadow price? How you can interpret it using the solution of part a? 2- Assume the following...