Consider an economy "I" with a representative household that consists of 1000 workers and owns $100...
Exercise 1. Production function model Consider an economy "I" with a representative household that consists of 1000 workers and owns $100 million of capital (L 1000, K -100). There is a representative firm with a Cobb- Douglas production function that rents capital and hires labor to produce. Assume that the TFP parameter equals one (A-1), we have Y K1/3L2/3. Markets are competitive. 1. Define an equilibrium in this economy. Follow class notes. 2. Solve for the equilibrium. You should get...
Consider a closed (no trade) economy "I" with a fixed labor force equal to 1000 and a fixed capital stock equal to 100 (L=1000, K=100). There is a representative firm with a Cobb-Douglas production function that rents capital and hires labor to produce. Assume that TFP parameter equals one (A=1) , we have Y=K^1/3 L^2/3. Markets are competitive. 1. graph the following: plot output per capita on the Y axis and capital per capita on the x axis. and show...
Consider a closed (no trade) economy "I" with a fixed labor force equal to 1000 and a fixed capital stock equal to 100 (L=1000, K=100). There is a representative firm with a Cobb-Douglas production function that rents capital and hires labor to produce. ASsume that TFP parameter equals one (A=1) , we have Y=K^1/3 L^2/3. Markets are competitive. 1. Solve for the equilibrium in this economy using the production function. You should get numbers for (Y,K,L,w,r). 2. Solve for the...
. Consider the following one-sector, closed, representative household economy. The production technology is given by the Cobb-Douglas production function where Y(t) is the output, K(t) is the capital stock, Lit) is the labor input, all at time t, 0 < a < and A(t) is the technology level at time t. Technological progress is at positive rate g. Let δ denote the depreciation rate for capital. This production function displays constant returns to scale in both K and L, hence...
. Consider the following one-sector, closed, representative household economy. The production technology is given by the Cobb-Douglas production function where Y(t) is the output, K(t) is the capital stock, Lit) is the labor input, all at time t, 0 < a < and A(t) is the technology level at time t. Technological progress is at positive rate g. Let δ denote the depreciation rate for capital. This production function displays constant returns to scale in both K and L, hence...
Just 5-8 1 Analytics of the Solow Model In the Solow economy, people consume a good that firms produce with technology Y (which we assume to be constant) and f is a Cobb-Douglas production function Af (K, L), where A is TFP f(K, L) KL-a Here K is the stock of capital, which depreciates at rate δ E (0, 1) per period, and L is the labor force, which grows exogenously at rate n > 0. Here employment is always...
Solow Growth Model D. Consider an economy with production characterized by function Y = AVKL, per capita output y = AVkt with rate of depreciation of capital 8, investment it = sy. = sAvky, capital transition function kt+1 - k = SAVk - Okt, where s is savings ratio. 1. Putting per capita output (income) y on the y-axis and k on the x-axis, graph the curves for depre- ciation and investment. Label steady state capital k* and steady state...
Competitive Equilibrium (10 pts) Consider an economy with a representative consumer, a representative firm, and a government. • The consumer can work up to h hours at an hourly rate of w. She only gets utility from consumption and does not care about how much she works. Their preferences are represented by the utility function U(C, l) = ln(C). The consumer also owns an exogenously given K units of capital, which they can rent to the firms at a price...
Let Y=10 * sqrt(K) * sqrt(L) Suppose households save 10% of all output. This savings is added to the capital stock for the next period. On the other hand, depreciation destroys 3% of capital in each period. Draw a graph depicting the steady state equilibrium. (You should have per capita capital on the x axis and per capita investment on the y axis.) Solve for the equilibrium, giving values for y*, k*, i*, and c*. Suppose the savings rate were to increase...
(f) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a production function x = f(k, l) = (kl)0.25and an unavoidable fixed cost equal to A. There are 100 consumers and, initially, 100 firms. Prices are w = v = Py = 1 and Px is determined in a competitive market. Representative consumer income is I = 2. In the long run,the number of firms is M (determined endogenously),...