Q2)
Consider two imaginary countries, indexed A and B. Each economy can be characterised by the model above, but the population is constant in both economies. In the steady state, GDP per worker in country A is 1.44 times that of country B and the ratio of physical investment to output is 0.3 in country A and 0.25 in country B. The rate of depreciation is the same in both countries. What must α be in order for the model to fit these facts?
Q3)
Consider the two countries A and B above, but modify the model along the lines of Mankiw, Romer and Weil (1992) so that human capital, H, is included as a factor input. For simplicity, labour efficiency is assumed to be 1 in both countries. Output in country i is thus given by
Yit = KitαHitβLi(1−α−β),
and capital is accumulated according to
∆Kit+1 = sikYit − δKit,
∆Hit+1 =shYit − δHit,
where we note that sh is the same in both countries.
A. Let y ≡ Y/L denote GDP per worker. Derive an expression for the steady-state value of the ratio yA/yB in terms of sAk, sBk, α and β.
B. Suppose that β = 0.5. What must α be in order for this model to fit the facts stated in Question 2?
answer is , alpha =
1/3
Consider the two countries A and B above, but modify the model along the lines of Mankiw, Romer and Weil (1992) so that human capital, H, is included as a factor input. For simplicity, labour efficiency is assumed to be 1 in both countries. Output in country i is thus given by Yit=Kαit Hβit Li(1−α−β) and capital is accumulated according to ∆Kit+1= sikYit−δKit∆Hit+1=shYit−δHit where we note that sh is the same in both countries. a. Let y ≡ Y/L denote GDP per worker. Derive an...
Q1)Consider a version of the Solow model where population grows at rate n. Assume that technology is Cobb-Douglas so that output is given by Yt = KtαLt(1−α).Capital depreciates at rate δ and a fraction s of income is invested in physical capital every period.A. Write down an expression describing capital accumulation in this economy and solve for the steady-state levels of capital and output per worker. Illustrate your answer in a diagram.B. How is steady-state capital per worker affected by...
pls solve parts f,g,h
Suppose Country X's initial capital per effective worker (K/AN) ratio is 16, while Country Z's initial capital per effective worker (KAN) ountries have the same production function: F(K, A,N) = 10K, 5(AN)05 (a) Derive the output per effective worker. The evolution of the capital stock is given by K +1 = (1 - 6)K, + I, where is the depreciation rate. (b) Derive and show that in the long-run growth model, the steady state capital per...
There are two countries, Anihc (country A) and Bapan (country B), with the same production function fk=5k0.5. However, country A has saving rates of 0.2, depreciation rate of 0.2 and population growth of 0.2; while country B has saving rates of 0.1, depreciation rate of 0.15 and population growth of 0.05. Using the Solow model: Find the steady state capital-labor ratio for each country. Find the steady state output per worker, and the steady state consumption per worker for each...
3.) There are two countries, Anihc (country A) and Bapan (country B), with the same production function . However, country A has saving rates of 0.2, depreciation rate of 0.2 and population growth of 0.2; while country B has saving rates of 0.1, depreciation rate of 0.15 and population growth of 0.05. Using the Solow model: a.) Find the steady state capital-labor ratio for each country. b.) Find the steady state output per worker, and the steady state consumption per...
Suppose that net exports, NXt, are determined by the following expression:NXt/Ȳt = αNX−βNX(rt−r∗t) (6), where Ȳt is potential GDP and rt−r∗t is the difference between the domestic and the foreign real interest rate. a. Explain the intuition behind expression (6). b. Modify the IS curve below so that (6) is taken into account. Ỹt= α − β (rt−r̃)It specifies a negative relationship between short-run output, Ỹt, and the real interest rate, rt c. Explain how a decrease in the domestic real interest rate affects...
WRITING MUST BE CLEAR TO READ!
3. Country A and country B both have the production function Y = F(K, L) = K^(1/3) L ^(2/3). 3a. Does this production function have constant returns to scale? Explain. 3b. What is the per-worker production function, y = f(k)? 3c. Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country...
1. Country A and country B both have the production function Y = F(K,L)= VKL. (5 Points) Does this production function have constant returns to scale? Explain. (5 Points) What is the per-worker production function, y=f(k)? (10 Points) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using...
1. Exercise 1. Predicting steady states and growth rates from Solow Model In this exercise, assume a = 1/3. Answer the following questions using the Solow model without population growth. a) First, assuming no differences in TFP. Assume that countries are in steady state. Following the Solow model, use the data in the table to predict the ratio of per capita GDP in each country relative to that in the US. Data Data Data Model (assume A = Aus) predicted...
Consider the Solow growth model. The production function is given by Y = K αN1−α , with α = 1/3. Depreciation rate δ = 0.05, and saving rate s = 0.25. Labor force grows at the rate n = 0.01. (a) Write down the law of motion for capital per worker. (b) Compute steady state capital per worker. (c) Suppose the economy has initial capital per worker k0 = 4. Describe the dynamics of this economy, i.e., how does capital...