A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce output y. The production function is f(x1, x2) = x11/2 + x21/2. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10.
(d) Does this production function exhibit increasing, decreasing or constant returns to scale?
(e) Solve the firm’s cost minimization problem. Derive the firm’s cost function c(y).
(f) Find the profit-maximizing choice of inputs x1* and x2* and output y*. Calculate the firm’s profit from these choices.
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A firm uses two inputs x1 and x2 to
produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce output y. The production function is...
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...
Company A uses 3 inputs (x1,x2,x3) to produce output Q. Nothing is produced unless some amount...
Company A uses 3 inputs (x1,x2,x3) to produce output Q. Nothing is produced unless some amount of input X3 is utilized. At the current level of X3, the output Q is produced according to the production function Q = x11/2x21/2 Denote the input prices by (W1,W2,W3) and assume the level of X3 cannot be varied in the time period under consideration but that X1 and X2 can be varied to whatever levels the firm desires. 1. Derive this firm’s total...
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.
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...
A firm wants to know how to minimize its costs for its new production plant, for...
A firm wants to know how to minimize its costs for its new production plant, for any desired level of output. Suppose the production is given by y = f(x1, x2) = 2 x11/2 x21/2, where x1 and x2 are inputs, and the input prices are w1 and w2. i. Sketch the cost minimization problem. Label your axes and graph appropriately. (1 point) ii. Find the optimal choices of x1 and x2. (2 points) iii. Find the cost function. (1...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 A) Does this firm's...
Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 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 xz? D) Suppose the firm wants to...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
Consider a two input firm which faces an aggregate technology for perfect compliments of y=min(3x1,x2). a....
Consider a two input firm which faces an aggregate technology for perfect compliments of y=min(3x1,x2). a. Plot isoquants for y=3,6 and 9 b. What are the returns of scale for this production function? c. For all possible prices on output, p, and on inputs, w1 and w2, are their price combinations for which a profit maximizing firm would not be able to select a price maximizing quantity (or at least one greater than 0)? Give a restriction on prices such...
2. Consider the following production function with two inputs X1 and X2. y = x1/2x2/4 a....
2. Consider the following production function with two inputs X1 and X2. y = x1/2x2/4 a. Derive the equation for an isoquant (assuming X2 is on the y-axis). b. Derive the marginal product of input x1. c. Derive the marginal product of input x2. d. Derive the marginal rate pf technical substitution (MRTS).
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...
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 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...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 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 xz? D) Suppose the firm wants to...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
2. Consider the following production function with two inputs X1 and X2. y = x1/2x2/4 a. Derive the equation for an isoquant (assuming X2 is on the y-axis). b. Derive the marginal product of input x1. c. Derive the marginal product of input x2. d. Derive the marginal rate pf technical substitution (MRTS).
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