You are running a small factory that uses labour (L) and capital (K) to produce output (Q). Your production function is Q space equals space 10 L to the power of bevelled 1 half end exponent K to the power of bevelled 1 half end exponent For every unit of labour you use you have to pay a wage of w - $ 20 and for every unit of capital you use you have to pay a rental rate of r = $5. You've signed a contract that you will produce Q-700 units of output. If you minimize your costs, what amount of labour (L) should you use?

You are running a small factory that uses labour (L) and capital (K) to produce output (Q). Your production function is Q space equals space 10 L to the power of bevelled 1 half end exponent K to the power of bevelled 1 half end exponent For every unit of labour you use you have to pay a wage of w - $ 20 and for every unit of capital you use you have to pay a rental rate of r = $5. You've signed a contract that you will produce Q-700 units of output. If you minimize your costs, what amount of labour (L) should you use?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

I need help on this question
Subpart 1-3
A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is: X=-0.2L3 + 18L2 + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A t what weekly output is marginal cost equal to average variable cost? if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?
The marginal product of labor can be determined using the total product of labor curve. Using the equation for the production function, the level of output when L = 8 and K = 25 is (3) 2³. (Enter a numeric response using a real number rounded to two decimal places). q=8LK+5L² Product or Output (q) 3,500- 3,000- 2,500- 2,000- 1,500- 1,000- 500- 0- Production Function 5 2 :8 15 15 10 Labor Input (L) 20 25
A firm produces basketballs with two variable inputs - labour (L) and plastic (K) - and has the following production function: f (L , K) = 6L1/3K1/6 If the price of output is 4, the price of labour is $2 and the price of plastic is $3, calculate the a) profit-maximizing level of each input b) the total production and c) the profit.
Please explain what numbers are being plugged in to get the answer.
Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in.
A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q). (d) Suppose wL = $25 and wM = $2. Determine the cost-minimizing combination of inputs if the baker wants to produce 200 mules. (e) Using wL = $25 and wM = $2 and the demand functions from part (c), write the firm’s long run cost function CLR(q).
Consider the "Cobb-Douglas" production function given by Y = AKº L¹-a where A> 0 and 0 < a < 1. Which of the following is FALSE? The marginal product of capital is positive The marginal product of labour is positive There is diminishing returns to capital O There is decreasing returns to scale
Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s costminimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.d) Determine this firm’s minimum cost of producing 120 units.e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s costfunction C(Q). Show your work.
Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is Q (K; L) = 4L^1/4 K^1/4 . Assume that the hourly wage of workers is fixed at $w and the price per machine is $r Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and r
Assume there is a linear isoquant where the input combination K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100? $20 $10 $50 $100