Economics 2150A/B Chapter Notes - Chapter 6: Diminishing Returns, Production Function, Marginal Product

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17 Nov 2017

School

Western University

Department

Economics

Course

Economics 2150A/B

Professor

Mohammad Iftekher Hossain

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ECON 2150A/B Full Course Notes

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Production function: mathematical representation of various technological recipes a firm can choose from to configure its production process. Tells us the maximum quantity of output the firm can produce given the quantities of input it might employ. Q = quantity of output, l = quantity of labor used, k = quantity of capital employed. Production function is analogous to the utility function in consumer theory, depends on exogenous technological conditions that may change over time (technological progress), and then the production function would shift. Points on or below the production function make up the firm"s production set, which is all the technically feasible combinations of inputs and outputs. Points inside the production set are technologically inefficient, the firm gets less output from its input than it could. Points on the boundary of the production set are technically efficient, the firm produces as much output as it possibly can given the amount of labor it employs.

Related Questions

A manufacturing firm's production function is Q = KL + K + L. The price r of capital services is equal to 1, and let w denote the price of labor services. If the firm is required to produce 5 units of output, for what values of w would a cost-minimizing firm use

a) only labor?

b) only capital?

c) both labor and capital?

plumturtle622

2. A firm plans to produce 1,000 units per day of good X. The firm's production engineer finds two technically efficient processes (i.e., input combinations of labor and capital) to produce 1,000 units per day:

Process 1 Process 2

Labor 10 8

Capital 20 25

a. If the production function for the existing technology is Q = f(L, K), where Q is the maximum possible output, L is the amount of labor used, and K is the amount of capital used, then f(10, 20) =__________ and f(8, 25) = ____________.

b. If the firm must pay $200 per day for a unit of labor and $100 per day for a unit of capital, which process is economically efficient?

c. If the firm must pay $250 per day for a unit of labor and $75 per day for a unit of capital, which process is economically efficient?

d. No matter what input prices prevail, as long as the firm employs either process 1 or process 2 it will be technically efficient. Evaluate this statement.

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A steel producer has the production function q=10K^0.75 E^0.25 where q is the quantity of steel, in metric tons, K is the firm's capital stock, and E is the number of labor hours it employs (measured in thousands). a) Assume the firm's current capital stock is fixed at K = 4096. If the firm employs E = 81 labor units, then how much steel does it produce?

b) Suppose the firm receives an order to produce 10,000 metric tons of steel. If its capital stock is fixed at K = 4096, then how many hours of labor must it employ to satisfy the order?

c) In the long run, the firm is free to vary both its capital stock and the number of workers it employs. Given this, what would happen to the firm's output if it doubles the amount of labor and capital it uses? What happens if it quadruples the amount? What does this result suggest in general?

Economics 2150A/B Chapter Notes - Chapter 6: Diminishing Returns, Production Function, Marginal Product

ECON 2150A/B Full Course Notes

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