3. Consider the linear production function y = axı + B.x2 where xı and X2 are...
3. Consider the linear production function y = ax + 3x2 where 21 and 22 are inputs with prices w; and w, respectively. (a) Derive the conditional factor demands for C and 22. (b) Derive the cost function (c) Derive the short-run cost function when input 2 is fixed at 22. (d) Derive both short and long-run average cost functions.
3. Consider the linear production function y a Br2 where aE1 and with prices w, and w respectively are inputs (a) Derive the conditional factor demands for and . (b) Derive the cost function (c) Derive the short-run cost function when input 2 is fixed at (d) Derive both short- and long-run average cost functions.
5. Let the firm's production function be given by y 1+2. Note that the inputs r1 and 2 are perfect substitutes in this production process. Suppose wi 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 of the second input, w2,...
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...
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...
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...
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...
Suppose that Jennifer produces good y by using input xi and x2. The production function which Jennifer faces is: y = x} + x3 The cost for every unit of xı is wi and the cost for every unit of x2 is w2. There is a fixed cost component F, which also forms a part of her total cost. (a) Write down the cost minimization problem. Solve this problem and express X1/X2 as a function of w2/w1.
please show all work, thanks! Problems 1 a) A firm has the production function y = 22212 and faces input prices W1 and w2. Derive the conditional input demand functions for both inputs. b) If W, = $5 and W2 = $10, what is the minimum cost of producing 27 units of output?
3. A firm's production function is given by y z1214. Input prices are wi and w2 Input 2 is fixed at 256. a) Derive the firm's variable cost function. b) Ifw1 8 and w2 5, what is the least cost of producing 40 units of output? c) At these prices and output, what is the marginal cost?