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EC111Class19Questions - fundamental neoclassical growth...

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EC111 MACROECONOMICS Spring Term 2012 EC111 Class 19 Question 1. The aggregate production function is Cobb Douglas, such that: Where Y is real national income T is an overall efficiency (or technology) term, K is the stock of capital and L is the stock of labour. a). Show that this production function exhibits constant returns to scale. b). Show that output per worker can be expressed as: where y is output per worker, Y/L, and k is capital per worker, K/L. c). Show that the change in capital per worker can be written as: d). Now suppose that saving is a constant proportion, 0.2, of income. Express the change in capital per worker, ΔK/L, as a function of T and k. There is no depreciation. e). Use the expression provided in (c) and the one you have derived in (d) to obtain the
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Unformatted text preview: fundamental neoclassical growth equation, when the rate of growth of the labour force ΔL/L is 0.02 (i.e.2 percent). f). Using the expression you have derived in (e) and assuming T = 1, find Δk when k = 64. Interpret your result using a diagram. g). Using the expression you have derived in (e) find the level of capital per worker in the steady state when T = 1. h). Is the savings rate in this economy the one that maximises consumption per worker in the steady state; in other words is this economy at the golden rule in (g) above? Question 2. a). Have incomes per capita in developed nations converged since 1950? b). How could we use the Solow model to explain that convergence?...
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