Consider an economy described by the following:

the production function is zK^{1/2}N^{1/2}

the utility function is C^{2/3}L^{1/3}

exogenous variables: K=1, G=0, h=1, Z=1.

- Write down the problem that the representative consumer solves. What is the solution to this problem?
- Write down the problem solved by the representative firm.
- Find the production possibility frontier for this economy. Explain what it describes.
- State the condition for an optimal allocation in this economy. Use it to find the optimal bundle(c,l). What is the equilibrium wage rate? Profits?
- What happen to the answer in d) if the productivity increases from Z=1 to Z=2?
- Draw a graph comparing the equilibrium in d) to that in e). What do you conclude? Explain.
- Is the consumer better-off if the government increases spending following the increase in Z? Explain.

this is my past midterm exam. I'm trying to solve the question for practice.

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