Suppose the production is characterized by the function Q(K,L) = 50K05L05. The price of labor is $5 and the price of capital is $20. Find the cost minimizing combination of capital and labor if the manufacturer has an order for 1000 units of output. Put differently, Given: Q = 50KO.5L0.5 w = $5, r = $20 Goal: Produce Qo = 1000 units of output as cheaply as possible.

Suppose the production is characterized by the function Q(K,L) = 50K05L05. The price of labor is $5 and the price of capital is $20. Find the cost minimizing combination of capital and labor if the manufacturer has an order for 1000 units of output. Put differently, Given: Q = 50KO.5L0.5 w = $5, r = $20 Goal: Produce Qo = 1000 units of output as cheaply as possible.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter7: Proudction Costs

Section: Chapter Questions

Problem 2SQ

See similar textbooks

Similar questions

What is the difference between a fixed input and a variable input?
A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.
Suppose that a food manufacturing company produces two goods, A and B, using the same plant and labor. The total cost of producing A and B is give by: (in the picture) Is this total cost function consistent with the present of increasing or decreasing returnsto scale
An electronics plant’s production function is Q = 5LK, where Q is its output rate, L is the amount of labor it uses per period of time and K is the amount of capital it uses per period of time. The Price of labor is $1 per unit of labor and the price of capital is $2 per unit of capital. a) What is the optimal combination of inputs the plant should use to produce 1000 units of output per period? b) Suppose that the price of labor increases to $2 per unit. What effect will this have on optimal L and K to produce Q=1000? c) Is this plant subject to decreasing returns to scale? Why or why not?
A manufacturer named Kjell is facing the following product function.1 x = f(N, K) = 100Nº.8K0,2 The price for labor is NOK 500 per unit. The price for capital is NOK 125 per unit. a) Does the product function provide constant, increasing, or decreasing scale benefits? b) Kjell wants to produce 400 cakes at the lowest possible cost. How much labor and does he need capital? What will be the cost? c) The bank is not impressed by Kjell's production technology. He therefore receives a loan of only NOK 1,875. How many cakes can Kjell produce a maximum of NOK 1,875. d) Make a factor diagram (N, K). Note Kjell's adaptation from problem b) and c). Draw the isocost lines and the substituent template. e) A short-term strike leads to the price of labor rising to NOK 750. Kjell still has only NOK 1,875. How will Kjell change his adaptation from c)?How many cakes does he produce now? f) Kjell eventually starts making money, and wants to expand production to 650 cakes. What will be Kjell's new…
A farmer uses a certain technology that produces electricity. His production function is given as: q = f (k, l) = 1000k¹⁰/20 – 201³ Where q is the no. of megawatts of electricity his company is producing. Suppose that their electrical generators, k=20, calculate for the following: 1. Marginal product of labor 2. Average product of labor if k=20 3. If k decreases from 20 to 17, calculate the new MP of labor and the average product. Explain intuitively what happens to the MP and the average product.
When do we say that a firm is operating with least cost combination of inputs?
The production function for the automotive and parts industry is q=L0 25 K0.16 M0.59 where M is energy and materials (based loosely on Klein, 2003). What kind of returns to scale does this production function exhibit? This production function exhibits constant returns to scale. The marginal product of materials, MPM, is O A. MPM = 0.59(q/M) O B. MPM = 0.59L0 25 K0.16M - 0.41 MPM =L0 25K0. 16MO.59 O D. both a and b. O E. all of the above.
Firm ABC has estimated that it has the following production function: Q = 1.5LK – 0.3L2 – 0.15K2 Labor (L) has a price of €60 and capital (K) has a price of €75. ABC wants to maximize the production with a total cost of €2025. (a) Determine the quantities of labor and capital the firm should use. (round results to 2 decimal places) (b) What quantity of output will be produced at the optimal combination of factors of production?