Question

Suppose an economy characterized by the following Cobb-Douglas production function: Y = K1/3L2/3. There are 1,000 units of capital and 1,000 employees in this economy. a) Derive an equation describing the demand for labor in the economy as a function of real wages and capital stock. b) If wages can move freely, what is the equilibrium real wage? What are the equilibrium employment, output and total wages in the economy? c) Assume that this economy has adopted a law that sets the minimum real wage equal to one unit of output. (The motivation of the law is to increase workers’ welfare.) How does the law affect employment, total output and total wages? Does the law improve the welfare of workers? Explain. How does your answer from d) depend on the elasticity of demand for labor? Can the answer to question d) be different? Use graphs to explain

Answer 1

In an economy with a Cobb-Douglas production function, the equilibrium real wage equates demand for labor with supply, determining employment and output levels. Introducing a minimum wage affects employment, output, and total wages and can lead to a loss of worker welfare if the minimum wage is set above the equilibrium. These effects depend on the elasticity of demand for labor.

Step-by-step explanation:

Given the Cobb-Douglas production function Y = K1/3L2/3, with capital K and labor L, we can derive the labor demand function. Employers determine their demand for labor based on the real wage they must pay and their current capital stock.

The equilibrium real wage equates labor demand with labor supply. In a free market, wages adjust to balance the quantity of labor demanded with the quantity of labor supplied, resulting in an equilibrium employment level and total output for the economy. The equilibrium real wage is found where the slope of the production function regarding labor equals the real wage rate.

Introducing a minimum wage equal to one unit of output may lead to unintended consequences, such as reduced employment if the minimum is above the equilibrium wage. The overall effect on worker welfare depends on whether the increase in wages for those still employed outweighs the loss of jobs.

The elasticity of demand for labor impacts these results. If labor demand is inelastic, employment changes little with wage changes, and total wages may increase. If labor demand is elastic, employment may fall significantly, and total wages may not increase.