A firm has the following production function: ?(?1, ?2) = ?1 + ?2 A) Does this...
A firm has the following production function:
?(?1, ?2) = ?1 + ?2
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A) Does this firm’s technology exhibit constant, increasing, or decreasing returns to scale?
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B) Suppose the firm wants to produce exactly ? units and that input 1 costs $?1 per unit and input 2 costs $?2 per unit. What are the firm’s conditional input demand functions?
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C) Write down the formula for the firm’s total cost function as a function of ?1, ?2, and ?.
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A firm has the following production function:
?(?1, ?2) = ?1 +
?2
A) Does this...
A firm has the following production function: ?(?1, ?2) = ???{?1, 2?2} A) Does this firm’s technology exhibit constant...
A firm has the following production function: ?(?1, ?2) = ???{?1, 2?2} 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 ? units and that input 1 costs $?1 per unit and input 2 costs $?2 per unit. What are the firm’s conditional input demand functions? D) Using the information from part D), write...
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...
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...
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...
Part 2: Short answer questions Question 1 (4 points): A sausage firm has a production function...
Part 2: Short answer questions Question 1 (4 points): A sausage firm has a production function of the form: q = 5LK+K+L where q is units per day, L is units of labor input and K is units of capital output. The marginal product of the two inputs are: MPL = 5K+1, MPK = 5L +1. Price per unit of labor: w= $15, price per unit of capital: v= $15. Both labor and capital are variable. a. Write down the...
For the production function F(L,K)=(L+K)^2 find whether the firm has constant, increasing or decreasing returns to...
For the production function F(L,K)=(L+K)^2 find whether the firm has constant, increasing or decreasing returns to scale. . A firm has monthly production function F(L,K) = L+√1+K, where L is worker hours per month and K is square feet of manufacturing space. A. Does the firm's technology satisfy the Productive Inputs Principle? B. What is the firm’s MRTSlk at input combination (L, K)? Does the firm’s technology have a declining MRTS? C. Does the firm have increasing, decreasing, or constant...
Consider a textile manufacturing firm that uses labor and capital inputs and has the production technology...
Consider a textile manufacturing firm that uses labor and capital inputs and has the production technology given by the equation Q = 8K0.25L 0.5 , where Q is output, K is capital and L is labor. Each unit of capital costs 10 TL while each unit of labor costs 5 TL. a) Does this firm have increasing, decreasing or constant returns to scale? (1) b) Define the cost minimization problem faced by firm. What is the objective function, what is...
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values...
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 K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
1a) A production function has the form f(a,b) = a^2 x b^3 . Does this function exhibit constant, increasing, or decreasing returns to scale? 1b)A production function has the form f(a,b) = 3a^1/2 x b^1...
1a) A production function has the form f(a,b) = a^2 x b^3 . Does this function exhibit constant, increasing, or decreasing returns to scale? 1b)A production function has the form f(a,b) = 3a^1/2 x b^1/2. Does this function exhibit constant, increasing, or decreasing returns to scale? Explain. Thank you.
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...
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...
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...
Part 2: Short answer questions Question 1 (4 points): A sausage firm has a production function of the form: q = 5LK+K+L where q is units per day, L is units of labor input and K is units of capital output. The marginal product of the two inputs are: MPL = 5K+1, MPK = 5L +1. Price per unit of labor: w= $15, price per unit of capital: v= $15. Both labor and capital are variable. a. Write down the...
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 K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
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