The Cobb-Douglas production function is commonly used to model the production of an output, based on two or more inputs. In this project, we will consider the inputs of capital and labour: • Capital, denoted by K, is the business's capital expenditures over a given time period. This could include money spent on space or equipment rental, maintenance, supplies, etc. • Labour, denoted by L, is the number of worker-hours used over the same time period. The output is the quantity of items produced, Q over the same time period. The key assumptions leading to the Cobb-Douglas production function are as follows. Assume Al and A2 are true throughout this individual project. A1. If the labour is held fixed, a very small relative change in labour K, AK should always lead to a corresponding relative change in Q that is proportional to the relative change in labour. In other words, AQ AK = a K (1) for some constant a > 0. A2. If the capital expenditures are held fixed, a very small relative change in labour L, 4, should always lead to a corresponding relative change in Q that is proportional to the relative change in labour. In other words, ΔL AQ Q (2)

The Cobb-Douglas production function is commonly used to model the production of an output, based on two or more inputs. In this project, we will consider the inputs of capital and labour: • Capital, denoted by K, is the business's capital expenditures over a given time period. This could include money spent on space or equipment rental, maintenance, supplies, etc. • Labour, denoted by L, is the number of worker-hours used over the same time period. The output is the quantity of items produced, Q over the same time period. The key assumptions leading to the Cobb-Douglas production function are as follows. Assume Al and A2 are true throughout this individual project. A1. If the labour is held fixed, a very small relative change in labour K, AK should always lead to a corresponding relative change in Q that is proportional to the relative change in labour. In other words, AQ AK = a K (1) for some constant a > 0. A2. If the capital expenditures are held fixed, a very small relative change in labour L, 4, should always lead to a corresponding relative change in Q that is proportional to the relative change in labour. In other words, ΔL AQ Q (2)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.14P

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