Question

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 Y_t = Kt^αL_t^(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 a decrease in the saving rate? Illustrate your answer in a diagram and provide intuition.

C. How  is steady-state capital per worker affected by a decrease  in the depreciation rate? Motivate your answer using a diagram.

Please provide an answer for A, B and C.

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?

Please provide an answer for this question.

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

Y_it = Kit^αH_it^βL_i^{(1−α−β)},

and capital is accumulated according to

∆K_it+1 = s_ikY_it − δK_it,

∆H_it+1 =s_hY_it − δH_it,

where we note that s_h 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 y_A/y_B in terms of s_Ak, s_Bk, 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?

Please provide an answer for A and B.

Answer 1

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Answer 2

Anyone with the answer to Q2 and Q3 as well please?