Assume the aggregate production is produced using the technology function Y = 2z√Nand 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?
Hint: Since the consumer doesn’t value leisure, he will optimally choose l? = 0. The MRS can not be calculated here and there is no need to use the MRS condition to solve for the optimal C? and l?
. When solving Question 4), use the definition of an equilibrium, that is, Ns = Nd.
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