2)The production function of a factory has the following characteristics:• Use workers (x1) and machines (x2).• It is not capable of producing if it does not contract one of the two factors of production,even if you hire the other.• You can increase production a given percentage, hiring the percentagemore workers without hiring more machines.• When you hire 1 worker and 1 machine, you can produce 8 per day.Which of the following production functions are consistent with the above and why?1/21/2a. y = 8x;'"x2"b. y = xx2%3D8c. y = min{8x1,8x2}d. y = min{x, x}%3D

Production function shows relationship between output and inputs.

Answered: 2) The production function of a factory…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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You are trying to figure out the multifactor productivity of your carrot farm. You had production of 436 pounds of carrots. You spent $1.50 per pound on fertilizer and used 2 pounds of fertilizer. Planting expenses were $50, and harvesting expenses were 190 hours at $10 per hour. What is your multifactor productivity, rounded to one decimal place?
In your "toast" production function, you used your labor and a toaster as capital. Keeping capital constant, i.e., with only one toaster if you keep adding the labor, i.e., bring your friends to help you with making toasts, which of the following might happen? Group of answer choices Marginal returns to labor will be a constant. Marginal returns to labor will keep decreasing and, after a point, it will become negative. Marginal returns to labor will keep increasing. Marginal returns to labor will keep increasing and then be a constant.
5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?
Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y = 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of production function called, and what are we assuming about the relationship between robots and pharmacists by using this production function? b. Derive the cost - minimizing demands for K and L as a function of output, the wage rate and the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10 materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale?f. The pharmacy plans to produce 40,000 prescriptions per week. At the…
You run a factory that uses pottery wheels to make pots. You can hire anywhere between 1 and 3 skilled artisans (workers), and you can rent 1 or 2 pottery wheels (machines). Pots sell for $125 each. The total product of your factory is shown in the following table. Number of Machines (Capital, K) 1 Pottery wheels are 2 1 8 10 Number of Workers (Labor, L) 2 11 14 3 13 17 Suppose you rent one machine and hire one worker. You would be willing to pay $ to hire a 2nd worker. (Consider the value of the marginal product of labor.) Suppose you rent one machine and hire one worker. You would be willing to pay a rental rate of up to $ Suppose the wage is $350. If you have one pottery wheel, the number of workers you would want to hire is to acquire a 2nd machine. (Consider the value of the marginal product of capital.)
Respond to the question with a concise and accurate answer, along with a clear explanation and step-by-step solution, or risk receiving a downvote.
A farmer has 1 acre of land. If he uses X pounds of fertilizer he can harvest √x tons of wheat. What is his production function if he has A acres of land and can just replicate the same production process on each piece of land? XXX A * A VXA √XA
6
Consider the following production function that depends only on labor:Q = 4L + 12L² - 6L³ 1. Compute the APL (average product of labor). 2. Compute the MPL (marginal product of labor). 3. What is the value of L* at which APL is the highest? 4. For L > L*, which one is bigger, APL or MPL? How about when L < L* and L = L*? 5. Draw APL and MPL on the y-axis as a function of L on the x-axis. Label the point of the intersection of APL and MPL.
Suppose that production function of certain devices is determined by: q = k * L - 0.8 k2 - 0.2 L2 Where q represents annual quantity of devices produced, k represents annual quantity of capital factor, and L represents annual quantity of labor factor. (a) Suppose k = 10; draw a graph with average and total labor productivity. What is level of labor (L) factor at which average productivity reaches a maximum? How many devices are produced at that point? (b) Assuming again that k = 10, plot Marginal Product (MP) curve. At what level do we have that labor (L) factor is MP = 0? (c) Suppose capital (k) factor were to increase to k = 20. How would your previous answers change?

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