Question

Directions: Answer ALL of the following questions. Show ALL calculations and present them in a neat and an orderly fashion. Credit will not be given for either unsupported answers or illegible answers. This is NOT a group assignment. Any indication of collaboration with your classmates will earn all involved a grade of zero (0). This assignment is due Monday, October 5, 2020. However, you may submit it before the due date. Late assignments are NOT accepted.

The following is information from the national income accounts for a hypothetical country:

GDP $6,000

Gross Investment 800

Net Investment 200

Consumption 4,000

Government purchases of goods and services 1,100

Government budget surplus 30

What is (are):

a. NDP?

b. Net exports?

c. Government taxes minus transfers?

d. Disposable personal income?

e. Personal saving?

In a simple scenario with only two factors of production, suppose that capital’s share of income is .4 and labor’s share is .6 and the annual growth rates of capital and labor are 6 and 2 percent, respectively. Assume there is no technical change.

a. At what rate does output grow?

b. How long will it take for output to double?

c. Now suppose that technology grows at a rate of 2 percent. Recalculate your answers to parts a and b.

Suppose output is growing at 3 percent per year and capital’s and labor’s shares of income are .3 and .7, respectively.

a. If both labor and capital grow at 1 percent per year, what would the growth rate of total factor productivity have to be?

b. What if both the labor and the capital stocks are fixed?

Consider the following production function:

Y = K.5(AN).5,

where both the population and the pool of labor are growing at a rate n = .07, the capital stock is depreciating at a rate d = .03, and A is normalized to 1.

a. What are capital’s and labor’s shares of income?

b. What is the form of this production function?

c. Find the steady-state values of k and y when s = .20.

d. (i) At what rate is per capita output growing at the steady state?

(ii) At what rate is total output growing?

(iii) What if total factor productivity is increasing at a rate of 2 percent per year (g = .02)?

Answer 1

GDP = $7000 GI = $800 NI = $200 C= $4000 G = $1100 Gs = $30

a.

NDP or the Net domestic product is given by deducting the depreciation amount from GDP. We obtain the amount of depreciation by the difference in gross investment and net investment.

Depreciation = GI-NI = 800-200 = 600

NDP = GDP - Depreciation = 7000-600 = 6400

b.

Net exports is generally given by exports-imports. This data is not provided here. However we do know the expenditure approach GDP equation given by Y=C+I+G+NX. We have all the components except NX here. So we can find NX as-

NX = Y-C-I-G = 7000-4000-800-1100 = 1100 is the required net exports.

c.

Now we want taxes-transfers. For this we should now that Budget surplus GS = T-G-TR

So, Gs + G = T-TR

T-TR = 30+1100 = 1130

d.

Disposable personal income is what remains of national income after paying for taxes and recieving transfers. Here we use NDP value as national income. We have got that taxes-transfer is 1130.

So DPI = NDP - T + TR = NDP - (T-TR) = 6400 - 1130 = 5270

e.

Personal saving = DPI - Consumption = 5270-4000 = 1270