Question 1
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.
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