L1/2 K1/2 – 1, supposeQuestion 4. (20 points) Consider the following production function: ythe prices of Labor and Capital are w and r respectively.What are the firm's conditional input demand functions (amount of K andL as a function of w,r,ythat minimizes the costs given the output)?

Cost is minimized when number of inputs are hired in such a way where marginal product per dollar of…

Answered: L1/2K1/2 – 1, suppose Question 4. (20…

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?
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5. Selpats produces pens with the production function f(k, l) = 200vkl. The price of capital is wk = 40 and the price of labor is wL = 10. (i) Determine the optimal input bundle for producing y pens in the long run and find the long-run cost function. (ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run. (iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run total cost function and the short-run marginal cost function. Explain the relationship between the short-run and long-run marginal costs when y = 10,000. (iv) Suppose that the price of output is p. Which value of y maximizes short-run profit? р.
1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes
Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3) The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.
Suppose a firm’s production function is ? = ?2?. a) Determine the labor and capital demand functions. b) Are capital and labor normal or inferior inputs in this production process?
Which of the following price elasticities of demand would indicate inelastic demand? 1 10 0.5
Please help solve for (b) what is long run cost in a?

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L1/2K1/2 – 1, suppose Question 4. (20 points) Consider the following production function: y = the prices of Labor and Capital are w and r respectively. What are the firm's conditional input demand functions (amount of K and L as a function of w,r,y that minimizes the costs given the output)?