IN CLASS ASSIGNMENT – 5 – OCTOBER 20 QUESTION-1: Consider the below model: 1YALKY Where A is the stock of ideas, LY is the amount of labour used in the production of the final good, K is the stock of capital and, is the constant between 0 and 1. the law of month of A is: ALAA , is constant between 0 and 1, LA is the labour devoted in the production new ideas. We assume 0 and 1 The resource constraint of the economy is: LLL YA and proportion devoted to both activities is constant: RA sL L and RYY ssL L 1 . The population grows at the rate of n i.e.: nLLL YA ˆˆˆ The capital accumulation for the physical capital stock is: YsK K . Depreciation is assumed to be zero. (a) Show that, at any time, the growth of technology, gA, is: LsAg RA 1 . Explain for each of the two cases: 1 and 1 how the output of the research sector A , the technological level A, and the technological growth rate Ag evolve over time when the labour input into the research sector LsL RA is constant. (b) Derive the equation for the growth rate of capital per worker as: n A kssk YK 1 1ˆ (c) Give an intuitive explanation of what the parameters and between zero and one imply. (d) Assume now that = 1 and =0. Write down the equation for the growth rate of A at the aggregate level, the growth rate of k =K/L and the growth rate of y=Y/L. (e) Define a balanced growth path (BGP) in this model. Assume that along a BGP the growth rates of LA and LY equal the rate of population growth (n). Derive the growth rate of A and y along the BGP. QUESTION-2: A) Suppose economy’s output is produced according to the production function given as: = ఈఊଵିఈିఊ where B is an index of technology change, E is energy (extracted) input in production which is equal to ௧ = . ௧ where se is energy extraction rate and Rt is initial energy stock, L is labor. Parameters and γ both are positive and between zero and one. Production function exhibits constant returns to scale in K, L and E. And, BgB BB ˆ , n L LL ˆ , and capital accumulation equation is dKsYK . From the bove model derive the growth rate of output per worker along the BGP as: ොீ = − ഥ[ + ] where 1 Bgg and ̅ = ቀ ఊ ଵିఈ ቁ B) Provide explanation by examining the growth rate of output per worker at the BGP for: (i) = 0 (ii) > 0 (iii) g = 0 i.e. no technological progress (iv) as population growth (n) increases.
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