1. What are the conditions necessary to achieve a steady-state equilibrium? (Hin

Question

1. What are the conditions necessary to achieve a steady-state equilibrium? (Hint: There are 3)

2. Go to the aggregate page in the Excel file. Find the steady-state equilibrium of the economy under the following conditions. Be sure to report the equilibrium interest rate and GDP/capita. Consumers live 4 periods make pre-tax labor income of 50,000 in the first period, 75,000 in the second period, 125,000 in the third period and 0 in period 4. They are born with 10,000 in assets. They also face a labor tax of 20 percent. The economy follows a Solow growth model where A= 2354.44, n=.20, and alpha = 0.3. You may use the same demographics that are given.(4 points)

3. What happens when the tax rate is increased from 20 to 25 percent? Find the new equilibrium under this different tax policy. Note: A= 2231.03 in this case. (3 points). Note some of the changes you see.

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In the previous question, the utility function was U(c1,c2,c3,c4) = ln (c1) + ln (c2) + ln (c3) + ln (c4). In this case, units of consumption are equally weighted in utility no matter when they occur. In reality, consumers tend to discount future values.

1. Let B be a number between zero and one and be the rate at which consumers discount utility in the next period. Rewrite the lifetime utilty of this 4 period household, including B. (Hint: Look at lecture notes, B is shown in the notes.) (3 points)

2. Assume the household earns income y1 in period 1. y2 in period 2, y3 in period 3, y4 in period 4, and the interest rate is r, write out the lifetime budget constraint for this household. (3 points)

3. Write out the Lagrange problem to solve for this houshold’s optimal choices? (2 points)

4. Derive the consumption function for this household. (2 points)

5. How does this consumption function compare to the standard consumption function? (2 points)

Explanation / Answer

Answer 1:

Various neo classical economists have given different interpretations of steady state growth rate of the economy. In steady state growth, all the variables like savings, investment, capital stock etc either grow at constant or at exponential rate in the economy.

1. Harrod stated that economy achieves steady state equilibrium when natural growth rate of the economy is same as the warranted growth rate of the economy.

2. Meade stated that in the state of steady growth , growth rate of total income and growth rate of income per head are constant with population growing at constant rate with no change in the rate of technical progress.

3. Solow stated that steady state growth is determined by expanding labor force and technical progress.

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