# ECON303-Intermediate Macroeconomic Theory

## Question 1 as learned in ECON303-Intermediate Macroeconomic Theory,

Assume the aggregate production is produced using the technology function Y = 2z √ N and the utility of the representative consumer is given by U(C, l) = ln(C).

This utility function implies, in particular, that the consumer does not value leisure. Let’s assume that G = T = 0. The consumer has a total number of h hours to split between leisure and work time.

1. Write down the consumer’s budget constraint.

2. Solve the consumer’s problem and solve for the optimal C ? and Ns .

3. Solve the firm’s problem and derive the optimal labour demand Nd .

4. Compute the equilibrium wage, consumption and employment in this economy.

5. How do these variables react to an increase in total productivity factor z?

## Question 2

Suppose households preferences are described by the utility function U(C, l) = 2β √ C + δl,

where C stands for consumption of market goods l stands for leisure, δ and β are positive constant parameters. The total number of hours available to the representative consumer is 1, and the market real wage is w.

Output is produced using the production function Y = z √ Nd , where z > 0 is the total factor productivity. In answering the first three questions assume, for simplicity that there is no government and π = 0

1. What are the optimal values C and l ?

2. Derive the labour supply and labour demand curves and graph them. Discuss if the income effect can ever dominate the substitution effect or not. [10 marks]

3. Compute the competitive equilibrium wage rate and employment for this economy.

4. Was it reasonable to assume a zero profit when solving the first three questions?

5. Now suppose that there is a government in this economy and its purchases are equal to G, where it finances them with imposing lump-sum taxes equal to T. Does the labour supply depend on G in the presence of the government. Why or why not? If G increases, how do output employment and employment respond? Explain clearly.