(b)- The production funeaKTor laptops of Patel is given by q = 10K°5 L°Swhere q is number of laptops produced per day, K is hours of machine time andL is labour hours. Patel's competitor Manish is using the production functionq = 10K L4.(i)If both companies use the same amount of capital and labor, which willgenerate more output?(i1)Assume that capital is limited to 9 machine hours, but labour is unlimitedin supply. In which company is the marginal product of labor greater?Explain.

The function of production in economics is to show an equation used between the number of factors of…

(b) The production funeaTor laptops of Patel is given by q = 10K° L°S where is number of laptops produced per day, K is hours of machine time and L is labour hours. Patel's competitor Manish is using the production function q = 10K L4 %3D If both companies use the same amount of capital and labor, which will generate more output? (i) Assume that capital is limited to 9 machine hours, but labour is unlimited in supply. In which company is the marginal product of labor greater? Explain. (ii)

(b) The production funeaTor laptops of Patel is given by q = 10K° L°S where is number of laptops produced per day, K is hours of machine time and L is labour hours. Patel's competitor Manish is using the production function q = 10K L4 %3D If both companies use the same amount of capital and labor, which will generate more output? (i) Assume that capital is limited to 9 machine hours, but labour is unlimited in supply. In which company is the marginal product of labor greater? Explain. (ii)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.8P

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A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a) What is the average product of labor, APL, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MPL, when capital is fixed at 36 units? (c) Suppose capital is fixed at 36 units. If the firm can sell its output at a price of $100 per unit of output and can hire labor at $40 per unit of labor, how many units of labor should the firm hire in order to maximize profits?
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solve d and(e)
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Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…
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Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.
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