Problem Set 4: Long-run Growth III Question 1: Growth Accounting for India Formally derive the growth accounting equation (2) that we presented in class on slide 5, lecture 4-2 (and which is equivalent to the one in the Goldman Sachs article in Appendix 1). Use it to replicate the data shown in the exhibits presented in class, i.e. estimate past TFP growth, and forecast future output growth. Question 2: Investment in Education Consider the Solow growth model with Cobb-Douglas production function, f(k) = Ak^h^1, where k denotes capital per worker and h human capital per worker. Suppose the savings rate is 20% and the depreciation rate is 10%. Besides, A = 1/2,  = 1/3 and h = 1. a) Derive the steady-state values of capital per worker and output per worker analytically. b) Consider a public education program that permanently increases public educational expenditures by 1% of GDP and that funds this additional spending by new borrowing. Suppose that these investments in education increase human capital per worker by 10% in the long run. Compute how this education program affects capital per worker and output per worker in the long run. Question 3: The Combined Solow-Romer Model Consider the combined Solow-Romer growth model with endogenous capital accumulation and production of ideas introduced in the lecture. a) Derive the long-run growth rate of aggregate production. b) How does the growth rate from part a) differ from the one in the Romer model without capital? How is the formula for an infinite geometric sum, 1++^2+^3+... = 1/(1),   (0, 1), relevant for the difference between the model versions with and without capital? c) Derive the level of long-run, aggregate production, Yt*, as a function of time t and exogenous parameters.