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5. Let the firm's production function be given by y = + x2. Note that the...
5. Let the firm's production function be given by y = x1 + x2. Note that the inputs 21 and 2 are perfect substitu...
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 1+2. Note that the inputs r1...
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,...
3. Consider the linear production function y = axı + B.x2 where xı and X2 are...
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.
4. A firm produces computers with two factors of production: labor L and capital K. It's pro- duction function is ....
4. A firm produces computers with two factors of production: labor L and capital K. It's pro- duction function is . Suppose the factor prices are wl = 10 and wK = 100. (a) Graph the isoquants for y equal to 1.2, and 3. Does this technology show increasing, constant, or decreasing returns to scale? Why? (b) Derive the conditional factor demands. (c) Derive the long-run cost function C(y). (d) If the firm wants to produce one computer, how many...
3. Consider the linear production function y a Br2 where aE1 and with prices w, and...
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.
4. A firm produces computers with two factors of production: labor L and capital K. It's...
4. A firm produces computers with two factors of production: labor L and capital K. It's pro- duction function is y 10 . Suppose the factor prices are wL = 10 and wk = 100. (a) Graph the isoquants for y equal to 1,2, and 3. Does this technology show increasing, constant, or decreasing returns to scale? Why? (b) Derive the conditional factor demands. (c) Derive the long-run cost function C(y). (d) If the firm wants to produce one computer,...
6. The production function of a firm is y = LIR. Labour is paid a wage,...
6. The production function of a firm is y = LIR. Labour is paid a wage, w = 1 and capital earns a rental rate, r = 2. (a) Derive the long-run conditional factor demands for L and K. (b) Derive the long-run cost function C(y). (c) If the firm operates in a competitive industry, p=me. Derive the long-run supply curve for the firm, y(p).
6. The production function of a firm is y = LIKt. Labour is paid a wage,...
6. The production function of a firm is y = LIKt. Labour is paid a wage, w = 1 and capital earns a rental rate, r = 2. (a) Derive the long-run conditional factor demands for L and K. (b) Derive the long-run cost function C(y). (c) If the firm operates in a competitive industry, p = mc. Derive the long-run supply curve for the firm, y(p).
3. Consider the linear production function y = ax + 3x2 where 21 and 22 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.
for context: Problem 1 Consider the production function + (e) Plot the long-run and short-run marginal...
for context:
Problem 1 Consider the production function + (e) Plot the long-run and short-run marginal cost curves. (f) At the point at which they intersect, is the long-run supply curve or the short-run supply curve more elastic? Problem 1 Consider the production function + (a) Assume for parts (a)-(d) that we are in the long run. Suppose the factor prices are wi = wy = 1. Show that the cost function is equal to (b) Suppose the market price...
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 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,...
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.
4. A firm produces computers with two factors of production: labor L and capital K. It's pro- duction function is . Suppose the factor prices are wl = 10 and wK = 100. (a) Graph the isoquants for y equal to 1.2, and 3. Does this technology show increasing, constant, or decreasing returns to scale? Why? (b) Derive the conditional factor demands. (c) Derive the long-run cost function C(y). (d) If the firm wants to produce one computer, how many...
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.
4. A firm produces computers with two factors of production: labor L and capital K. It's pro- duction function is y 10 . Suppose the factor prices are wL = 10 and wk = 100. (a) Graph the isoquants for y equal to 1,2, and 3. Does this technology show increasing, constant, or decreasing returns to scale? Why? (b) Derive the conditional factor demands. (c) Derive the long-run cost function C(y). (d) If the firm wants to produce one computer,...
6. The production function of a firm is y = LIR. Labour is paid a wage, w = 1 and capital earns a rental rate, r = 2. (a) Derive the long-run conditional factor demands for L and K. (b) Derive the long-run cost function C(y). (c) If the firm operates in a competitive industry, p=me. Derive the long-run supply curve for the firm, y(p).
6. The production function of a firm is y = LIKt. Labour is paid a wage, w = 1 and capital earns a rental rate, r = 2. (a) Derive the long-run conditional factor demands for L and K. (b) Derive the long-run cost function C(y). (c) If the firm operates in a competitive industry, p = mc. Derive the long-run supply curve for the firm, y(p).
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.
for context:
Problem 1 Consider the production function + (e) Plot the long-run and short-run marginal cost curves. (f) At the point at which they intersect, is the long-run supply curve or the short-run supply curve more elastic? Problem 1 Consider the production function + (a) Assume for parts (a)-(d) that we are in the long run. Suppose the factor prices are wi = wy = 1. Show that the cost function is equal to (b) Suppose the market price...
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