Question

Question 5. (4 points each) Consider the Solow model in Chapter 6. Production function is given by Y = A_KENZ The notations of variables are the same as the slides for Ch.6.The depreciation rate d is 0.1, the population growth rate n is 0.1, and the saving rate s is 0.2. The level of productivity is constant, so At = 2 all the time. (1) Compute the steady-state level of capital per person k*. (2) Compute the steady-state level of output per person yº. (3) Compute the steady-state level of consumption per person c*. (4) What is the growth rate of total output Yt at the steady-state? (Hint: Yt = y Nt. See Ch.6 Part 1 Slide 5 about how to compute the growth rate of a product of two variables.) (5) What is the Growth Accounting equation for this economy? Apply the equation to this economy when the economy is at the steady-state, i.e. what is the contribution of capital, labor, and productivity to the growth rate of total output Yt at the steady-state respectively? (Hint: You simply need to express the production function in growth rates. See Ch.6 Part 1 Slide 21.) (6) Suppose the government wants to maximize consumption per person at the steady-state by changing the saving rate s. Compute this saving rate (i.e. Golden rule saving rate) that maximizes consumption per person and the associated consumption per person. (Hint: Express c* in terms of parameters including s. Then, take the derivative of c* with respect to s to maximize c.) (7) Is the policy to change saving rate from 0.2 to the one you find in question (6) always good for households? Explain a potential problem if any. (Hint: Consider the transition from the steady-state in question (3) to the steady-state in question (6). What happens to Ct during the transition, especially immediately after s changes?)

Answer 1

As per the HOMEWORKLIB POLICY, answering the first four parts.

Y == Aki Nike , At=2 Y+= 2K1² NZ (1) oup output - per worker Yt - NE [de = 2 kk 2 o at steady-state, Akt = 0 sf (ke) - (d+n) kt = 0 0.2 (akº?) - (01 + 0.1) Rt = 0 » 0.4R12 = 0.2ke Q = km2 [kE = 4 Any (2) Put Rid in ean. O 94 = 2x (4)62 = [(ar) "? Y+= 2x2 - Ty* = 4 Ano (3) steady - state consumption per peopun (c): v = (1-8) y = (1+0.2) x4 Ich = 3.2 Ano (4) Y = 48 X NE dog Yx = log yt + logNt (taking leg both sides) → Rate of Goowth in toted Output = Goouth Rale in output per worker + Growth Rete in population - Total output Growth Rate = of 0.1 = 0.1 A