5. Suppose that the economy's production function is Y = √K√LA where K is capital, L is labor, and A is the state of technology. Suppose that the saving rate (s) is equal to 2.4%, the rate of depreciation of capital (5) is equal to 3%, the number of workers grow at 0.7% per year and the rate of technological progress is 3%. (a) Find the steady state values of: iv. v. growth rate of output per worker growth rate of output (b) Suppose that the growth rate of workers decreases. What is its short-run and the long-run effect on the growth rate of output per worker ?
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- Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].c. You are given the following information about an economy. Y = C + I Y = F(K, L) The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns. s = saving rate (assume this is constant) per year δ= depreciation rate (assume this is a constant) per year y = Y/L k = K/L k* = steady state of capital per worker (K/L) and sf(k) < δk. i. What is sf(k) ii. What is δk? iii. Interpret the meaning of sf(k) < δk?
- Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Show the steady state in a graph. In the same graph, show the effect of a decrease in the depreciation rate, say to 2%Assume that total output is determined by this formula: number of workers × productivity = total output Hint: Assume there are 100 workers and each worker produces $100 of output. If productivity increases by 3 percent and the number of workers increases by 2 percent a year, how fast will output grow?Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.
- 16 True or False? The key difference between the Solow and production/expenditure models of the economy is that the Solow model endogenizes the saving rate.Computing growth rates (II): Suppose k, l, and m grow at constant rates givenby g k, gl , and gm. What is the growth rate of y in each of the following cases?(a) y = k 1/3(b) y = k 1/3l 2/3(c) y = mk 1/3l 2/3(d) y = mk 1/4l 3/4(e) y = mk 3/4l 1/4(f ) y = 1klm2 1/2(g) y = 1kl2 1/4 11/m2 3/4Suppose that the production function of a company is given by q = qL^2 · qC and that the amount of labour qL and the amount of capital qC are functions of time t. At time t = 2, we know that qL = 9 andqC =8 and that the growth rateof qL is equal to 2 and the growth rate of qC is equal to 8. Find the growth rate of the production q at that moment.
- In class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic consequences of decreasing the savings rate in this economy? • (c) What would be the consequences of an increase in fertility in this economy? • (d) Would the consequences of decreasing fertility be UNAMBIGUOUSLY GOOD? • (e) Can human capital grow without bounds? Explain why or why not (make sure you discuss the physical nature of human capital). • (f) What is the growth rate of the economy (in the absence of technological progress) if human capital cannot grow without bounds?1.Many countries, including Pakistan, import substantial amounts of goods and services from other countries. However, economists claim that a country can enjoy a high standard of living only if it can produce a large quantity of goods and services itself. Can you reconcile these two facts? (Maximum 100 words). 2.Given the production function Y= AF (L, K, H, N), explain the determinants of productivity. ( Maximum100 words). 3.Population growth has a variety of effects on productivity. Explain this statement and justify your answer. (Maximum 200 words).21.According to some modern theories of long run economic growth, successive increments of investment have________ returns since some fixed costs are ________ for subsequent firms.A. constant; identicalB. increasing; higherC. increasing; lowerD. decreasing; higher