Problem 3: A firm has the following production function: f(x1,x2) = x7/3x4/3 A) Does this firm's...
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 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 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...
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 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...
A firm has decreasing returns production function f(x1, x2)=(x1)1/6(x2) 1/3 and faces input costs w1=1 and w2=2. Find the cost function.
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....
A firm has the following production function: ?(?1, ?2) = ?1 + ?2 A) Does this firm’s technology exhibit constant, increasing, or decreasing returns to scale? 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? C) Write down the formula for the firm’s total cost function as a function of ?1, ?2, and ?.
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).