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11 Dec 2019

INTERMEDIATE MACROECONOMICS: SOLOW GROWTH MODEL

Hello. I have already made a graph, but I am confused by parts (d) and (e). Thanks for your help! Here is the problem:

Assume no technological progress. Draw the Solow Growth Model. This should include (in per-worker terms), the production function, the savings (i.e., investment) function, and break-even investment function. Label everything appropriately.

a. Label the steady-state levels of capital per worker and output per worker as k*0 and y*0, respectively. .

b. Suppose population growth increases. Show this change on your graph. Label the new steady-state levels of capital per worker and output per worker as k*1and y*1, respectively.

c. Explain what happens to the economic growth rate gY in the transition from y*0 to y*1. (i.e., is negative, zero, or positive and why?)

d. Explain what happens to the economic growth rate gY at y*1. (i.e., is negative, zero, or positive and why?)

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Casey DurganLv2
12 Dec 2019
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Related questions

Country A has the production function: Y = F (K, L) = K0.5L0.5

a. Express the production function in per worker terms. Thus, y = f (k) where y = Y/L and k=K/L

b. Suppose that both countries start off with a capital stock per worker of 2 (i.e. k = 2). What are the levels of income per worker and consumption per worker? Illustrate this on a graph

c. Assume that neither country experiences population growth or technological progress. Assume further that country A saves 10 percent of its output and the stock of capital depreciate by 5 percent each year. Using your answer from part (a) and the steady-state condition that investment equals depreciation

i. Find the steady-state level of capital per worker for each country.

ii. Find the steady-state levels of income (output) per worker and consumption per worker for each country

iii. Show on a graph the steady-state capital stock per worker, output per worker and consumption per worker for each country

d. State the condition for the Golden Rule and find the Golden Rule level of capital.

Suppose the output per effective worker is production function is y=10k1/2, where k equals the amount of capital per effective worker and the capital lasts an average of 10 years. Assume that the saving rate is 32 percent, the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.

a) Solve for the steady state levels of capital per effective worker, output per effective worker, investment per effective worker and consumption per effective worker.

b) Calculate the growth rate of total capital income and the growth rate of total labor income at the steady state.(Hint: Capital and labor each earn a constant share of the economy's income ).

c) Prove, at the steady state, (i) the capital-output ratio is constant;(ii) the real wage grows at the rate of 2 percent.

d) Calculate all of the following at their Golden Rule levels: Capital per effective worker, output per effective worker, saving and investment per effective worker, and the consumption per effective worker.

e) Whether the saving rate is too high or too low?

Country A and country B both have the production function:

Y = F(K,L) = K^(1/3)L^(2/3).

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

b) What is the per-worker production function, y = f(k)

c) Assume that neither country experiences population growth nor technological progress and that 20-percent of capital depreciates each year. Assume further that country A saves 10% of output each year 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?

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