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Economics

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1. This problem requires the use of calculus to solve some consumer

optimization problems

 1) Nina has the following utility function

? ? ln?????ln?????ln????
 

She starts with wealth of $120,000 earns no additional income, and faces a zero interest rate. How much does she consume in each of the three periods (Hint: The marginal rate of substitution between consumption in any two periods is the ratio of marginal utilities).

 2) David is just like Nina, except he always gets extra utility from present consumption. From the perspective of period one, his utility function is

? ? ?ln?????ln?????ln????

In period one, how much does David decide to consume in each of the three periods? How much wealth does he have left after period one?

2. Suppose that people’s expectations of inflation are subject to random shocks. That is, instead of being merely adaptive, expected inflation in period t, as seen in period t-1, is ?? ? ??? ? ?? ? ? ??? ? ?

, where ?? ? ? is a random shock. This shock is normally zero, but it deviates from zero when some event beyond past inflation causes expected inflation to change.

Similarly, ???? ? ? ? ?? ???.

 1) Derive both the dynamic aggregate demand(DAD) equation and the dynamic aggregate supply(DAS) equation in this slightly more general model.

 2) Suppose that the economy experiences an inflation scare. That is, in period t, for some reason people come to believe that inflation in period t+1 is going to be higher, so ?? is greater that zero(for this period only).

What happens to the DAD and DAS curves in period t? What happens to output, inflation, and nominal and real interest rates in the period?

Explain.

 3) What happens to the DAD and DAS curves in period t+1? That happens to output, inflation, and nominal and real interest rates in that period? Explain.

 4) What happens to the economy in subsequent periods?

 5) In what sense are inflation scares self-fulfilling?

3. Use the neoclassical model of investment to explain the impact of each of the following on the rental price of capital, the cost of capital, and investment.

 a. Anti-inflationary monetary policy raises the real interest rate

 b. An earthquake destroys part of the capital stock.

 c. Immigration of foreign workers increases the size of the labor force.
 

1. Country A and country B both have the production function

? ? ???? ?? ? ?

????

???

 a) Does this production function have constant returns to scale?

 b) What is the per-worker production function, ? ? ?????

 c) Assume that neither country experiences population growth or technological progress and that 20% of capital depreciates each year. Assume further that country A saves 10% and country B saves 30% of output each year. Using your answer from part b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country.

Then find the steady-state levels of income per worker and consumption per worker.

 d) Suppose that both countries start off with a capital stock per worker of 1.

What are the levels of income per worker and consumption per worker?

2. An economy has a Cobb–Douglas production function:

? ? ?

?????

? ? ? The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in steady state.

 a. At what rates do total output, output per worker, and output per effective worker grow?

 b. Solve for capital per effective worker, output per effective worker, and the marginal product of capital.

 c. Does the economy have more or less capital than at the Golden Rule steady state? How do you know? To achieve the Golden Rule steady state, does the saving rate need to increase or decrease?

 d. Suppose the change in the saving rate you described in part (c) occurs.

During the transition to the Golden Rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)? After the economy reaches its new steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)? Explain your

answers.