Suppose the process of producing lightweight parkas by Polly's Parkas is described by the functionq=40K04(L-40)0.6where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L thenumber of person-hours of labor. In addition to capital and labor, $40 worth of raw materials is used in theproduction of each parka.Note thatandдаак=40(0.4)K 0.60 (L-40)0.6да=40K04 (0.6)(L-40) 0.4-0.40aLBy minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a functiof output (q), wage rates (w), and rental rates on machines (r).The cost-minimizing demands for K and Lare

Answered: Suppose the process of producing…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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For the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for |å| and use it to answer the question. (a) Maximize P = 2000L3/5K2/5 with budget constraint 15L + 32OK = 8000. L = K = P = (b) Evaluate and give an interpretation for |21. Each additional dollar of budget increases production by this amount. (c) Approximate the increase in production if the budget is increased by $80. units
Show using math and logic that for constant returns to scale production functions, MRTS between labor and capital depends only on the K/L ratio, and not the scale of production.
complete the table
Kris wants to open a BBQ restaraunt. He has signed a 12- month lease at $6,000 per month. The lease enabled him to rent a restaraunt with all the equipment he needs to make BBQ; therefore, K equals 1. Kris must pay his workers a monthly salary of $2,400 each. His production function is q = 100L1/2K1/2 where q is the quantity of BBQ prepared per month in pounds, L is the number of workers employed per month, and K is the quantity of capital employed, and, as previously indicated, K is assumed to equal 1. What does Kris's monthly total cost expressed as a function of quantity equal?
Question 37 [ DIFFICULT] Consider two firms, both producing the same product, using the same production technology given by: q = √√K This production technology implies the following MRTS: K MRTS=AY ΔΧ L where K is the amount of capital used and L is the amount of labour used to produce output. It can be shown that this production technology implies the following minimised total cost function: TC = 2q√w√r where w represents the per-unit cost of labour and r represents the per-unit cost of capital. Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90 units of output. One firm (Firm 1) chooses its input combination to minimise costs of production. However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to Firm 1, how much higher are Firm 2's cost of production? a) $270 b) $67.50 c) $275 d) $135 e) $132 Hint: It can be shown that the cost-minimising quantities of capital and labour (chosen by Firm 1) are K = 30…
please show graphs and table thank you
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
Suppose that Flamerock Tires must decide where to produce one million tires: the US, where wages are 30 and the cost of capital is 5; or China, where wages are 5 and the cost of capital is 25. Production in each location follows the same technology (production function) given by: Q = f(L, K) = L^0.25 K^0.75 Computationally solve the cost - minimizing input levels in each location to produce the goal of 1 million tires
Seton is interested in reducing costs while maintaining quality and patient satisfaction. You have been hired by the Seton Hospital System to improve efficiency. In particular, Seton believes that it is not efficiently combining physician labor hours (L) and physical capital units (K) in producing stent surgeries. Assume that we know that the production function is Q = KL. Assume that the price of L is $1/hr and the price of K is $4 per unit. a. How might Seton use more capital and less labor to install the same stent? What does that real-life tradeoff look like? b. We are going to find the cost minimizing way of producing 100 stent surgeries at Seton. Begin by drawing yourself a picture of how you will solve this problem. Place K on the vertical axis and L on the horizontal axis. c. Write the budget constraint and find the equation of the slope of this line (dk/dL)
A software firm has only two inputs to production: domestic programmers based in the firm's U.K. office and international programmers working from home in low-cost countries. The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is: S=2D + I Where S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible. (a) The firm must produce 10 pieces of software this year. Show the firm's isoquant in a suitably labelled graph. Put "domestic programmers" on the vertical axis and "international programmers" on the horizontal axis. Label each axis from 0 to 10. (b) A domestic programmer can be hired for £100,000 per year. An international programmer can be hired for £60,000 per year. On the same graph, show the different combinations of…
Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.
The quantity, Q, of a certain product manufactured depends on the quantity of labor, L, and of capital, K, used according to the function 0 = 900LK¹³. Labor costs $100 per unit and capital costs $50 per unit. What combination of labor and capital should be used to produce 36,000 units of the goods at minimum cost? What is that minimum cost? Round your answers to two decimal places.

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