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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 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,...
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 = + 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...
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.
A producer produces good y using inputs x1 and x2 according to the production function y...
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...
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.
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's tec...
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in x1. Is the marginal product of input 2 increasing, constant, or decreasing in x2? D) Suppose the firm...
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.
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does...
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
A firm has the production function y= f(x1,x2)= 0.25x11/2 x21/2 . Input prices are w1=$4 and w2=...
A firm has the production function y= f(x1,x2)= 0.25x11/2 x21/2 . Input prices are w1=$4 and w2= $16 a) Use the technical rate of substitution, the input price rate, and the production function to compute the conditionial input demand fucntion x1(y) and x2(y). b) Compute the firm's long run cost function c(y).
Problem 1: A firm has the following production function: min{x1, 2x2) f(x,x2)= A) Does this firm's technology exhibit c...
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...
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 = + 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.
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...
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.
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in x1. Is the marginal product of input 2 increasing, constant, or decreasing in x2? D) Suppose the firm...
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.
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
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...
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