Assume an economy populated with two types of fiats-production firms and rental

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Assume an economy populated with two types of fiats-production firms and rental firms. Production firms rent capital K from rental nominal price R. Production firms also hire labor L at nominal wage W in order to produce their output P that they sell at nominal price P. The production function of production firms takes the following Cobb-Douglas form: Y = 0.5k^0.5 L^0.5 The key decision for production firms is how much capital K to rent from rental firms. On the other hand, rental firms rent capital /ti to (action firms for nominal price R. Their nominal costs are given by P_kk(r + rho), where r is the real interest rate and rho is the depreciation rate. The key decision of rental firms is how much capital K to buy m market price P_k Derive the function for demand for capital K^D on the part of production firms that maximizes their profits (real or nominal). This will be a function of the real rental rote of Capital. Show that k^D is a negative function of the real rental rate R/P.Assume that L=100 and that p_k/p(r + rho) = 1.5. Derive the steady state value for the capital stock k* (Remember that this is the point at which the rental firm is exactly indifferent between increasing or decreasing capital). Suppose that there is a surge in the population and L increases to 225. Fast, solve for the value of the real rental rate, R/P, with this new level of L,but with your value of K from part (c)(remember that R/P= MPK). Then, solve for the new steady state value of the capital stock K*, and the new steady state value of the real rental rate, r/p. If Here are no changes in the costs of supplying capital, describe how investment will behave immediately after the population surge and m the economy gradually approaches the new steady state level of capital.

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Assume an economy populated with two types of fiats-production firms and rental

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