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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,...

Consider an economy described by the following:

 the production function is zK1/2N1/2

 the utility function is C2/3L1/3

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

  1.  Write down the problem that the representative consumer solves. What is the solution to this problem?
  2.  Write down the problem solved by the representative firm.
  3.  Find the production possibility frontier for this economy. Explain what it describes.
  4.  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?
  5.  What happen to the answer in d) if the productivity increases from Z=1 to Z=2?
  6. Draw a graph comparing the equilibrium in d) to that in e). What do you conclude? Explain.
  7.  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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