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.
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A producer produces good y using inputs x1 and x2 according to
the production function y...
Suppose that Jennifer produces good y by using input xi and x2. The production function which...
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.
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10. (5 points) (w1, w2) respec- (2) Suppose that the price of product is p, and that the prices of factors are tively. Find the factor demand function ri(w, w2, p), x1(w1, w2, P), the supply function y(w1, W2, P), and the profit function T(w1, w2, p). (10 points)
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
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.
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...
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...
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...
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production functio...
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 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...
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).
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...
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.
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10. (5 points) (w1, w2) respec- (2) Suppose that the price of product is p, and that the prices of factors are tively. Find the factor demand function ri(w, w2, p), x1(w1, w2, P), the supply function y(w1, W2, P), and the profit function T(w1, w2, p). (10 points)
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
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.
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...
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...
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...
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...
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...
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