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…

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section7.A: Appendix: A Closer Look At Production And Cost

Problem 1AQ

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Suppose a firm uses capital K and labor L to produce output Q with the following production function: 1 Q=4KL + = 1² 3 (a) Find the marginal product of capital and the marginal product of labor. (b) Find the average production of capital and the average production of labor. (c) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (d) Find the marginal rate of technical substitution (RTS). (e) Use your result in (d) to find the elasticity of substitution. (f) Find the contingent demand functions for capital and labor if w is the price of labor input and v is the price of capital input.
E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3D
b) Suppose a company has this Leontief production function Q = min(20K,50L) i) List a few combinations that will produce 500 units of output
1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?
100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
*0.65 0.35 where x is the amount of labor and y is the amount of capital. The productivity of a country is given by f(x,y) = 100x (a) Compute the marginal productivities of labor and capital when x = 300 and y = 500. (b) Use part (a) to determine the approximate effect on productivity of increasing capital from 500 to 502 units, while keeping labor fixed at 300 units. (c) What would be the approximate effect of decreasing labor from 300 to 298.5 units while keeping capital fixed at 500 units? (a) The marginal productivity of labor is (Do not round until the final answer. Then round to two decimal places as needed.) The marginal productivity of capital is (Do not round until the final answer. Then round to two decimal places as needed.) (b) When capital is increased from 500 to 502 units, the approximate change in productivity is (Do not round until the final answer. Then round to two decimal places as needed.) (c) When labor is decreased from 300 to 298.5 units, the approximate change…
Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL3
(v) Find the ratio of the marginal productivities of two inputs, at L=2 and K =3 when the production function is given by Q= 8LK- L2 -K?
(3) A firms production function is Q(L) =15L -0.1L, where output (Q) is a function of a single input labour (L). (i) Find the number of workers required to maximize total product. (ii) For what number of workers is average product maximum?
Al's production function for deer is f(x1,x2) = (2x1 + x2)^1/2, where x1 is the amount of plastic and x2 is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $3 per unit, then the cost of producing 5 deer is a) $55 b) $10 c) $50 d) $75
A firms production function is Q(L)=15L2-0.1L3, where output (Q) is a function of asingle input labour (L).(i) Find the number of workers required to maximize total product.(ii) For what number of workers is average product maximum? Answer all please and thank you.
Suppose the production function for good q is given by q = (k+1)¹/2 where k and I are capital and labor inputs: (a) The function exhibits diminishing marginal productivities in both inputs. (b) The function exhibits diminishing marginal productivities in capital but not in labor. (c) The function exhibits diminishing marginal productivities in labor but not in capital. (d) The function exhibits increasing marginal productivities in both inputs.

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