A farmer can produce f(x,y) = 208-√4x² + y² units of produce by utilizing x units of labor and y units of capital.(a)(b)(c)Calculate the marginal productivities of labor and capital when x = 12 and y = 10.Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 12 to 12+h units while keeping capitalfixed at 10 units.Use part (b) to estimate the change in production when labor decreases from 12 to 11.5 units and capital stays fixed at 10 units.(a) The marginal productivity of labor when x = 12 and y = 10 is(Simplify your answer.)

To calculate the marginal productivity of labor at a specific point, we can take the partial…

Answered: A farmer can produce f(x,y) = 208-√4x²…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Which of the following production functions exhibits constant returns to scale (refer to activities and slides ): Group of answer choices q = AL0.5K0.6 q = AL0.3K0.4 q = AL0.5K0.7 Q = 10 L0.3 K0.7
A T-shirt screener can screen t-shirts (q) in two different ways. He can either use a fast screening machine (F) or a slow screening machine (S). Screen use is defined in terms of ”hours” running. His production function is f(F, S) = 10F + 6S. (a) The screener wants to be able to produce 120 shirts. List three feasible and efficient production plans (combinations of inputs) for doing this. (b) Graph the screener’s isoquant curve for q = 120. (c) The hourly cost of using the fast machine is $800 and the hourly cost of the slow machine is $200. What is the cost minimizing (optimal) combination of inputs for producing 120 shirts? (d) Suppose the screener must now produce 400 shirts. What is the cost minimizing combination of inputs?
Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL3
Given the following production function: q = 10KL. Assume that w = 25, r = 75 and C = 1200. (a) Mathematically find the minimum cost combination of capital and labour to produce a given level of output.b) Does the production function in part (a) show increasing returns to scale, decreasing returns to scale, or constant returns to scale? Explain. (c) Using isoquants and isocosts, graphically illustrate the effect of an increase in the wage rate, assuming the firm is producing at the same level of output.
can you please provide explanations and working
***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…
Provethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scale
F. None of the above 4) Please indicate whether the following production function has the characteristic of CRS, IRS and DRS. (b) F(K, L)=[aKP +(1-a)Le ]1/e, (1>a>0, 1>p) 1. CRS 2. IRS 3. DRS 4. None of the above
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?

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