Consider a Production Function for an Economy

question 102

Essay

Consider a production function for an economy:
Y = 20(L^.5K^.4N^.1)
where L is labour, K is capital, and N is land. In this economy, the factors of production are in fixed supply with L = 100, K = 100, and N = 100.
​
a.What is the level of output in this country?
b.Does this production function exhibit constant returns to scale? Demonstrate by example.
c.If the economy is competitive so that factors of production are paid the value of their marginal products, what is the share of total income that will go to land?​

---

Definitions:

Cost Function

An equation that calculates the total cost of producing goods or services as a function of the quantity of output produced.

Production Function

A mathematical relation that expresses the relationship between inputs used in production and the output produced.

Minimizing Unit Costs

The process of reducing the cost per unit of production in order to achieve greater efficiency and profitability.

Price Ratio

The proportional relationship between the prices of two goods, indicating how many units of one good can be exchanged for one unit of another good.