Consider an economy whose production function is Y = Kθ(AN)1–θ with A = 4K/N. Suppose that...

Consider an economy whose production function is Y = Kθ(AN)1–θ with A = 4K/N. Suppose that it has a savings rate of 0.1, a population growth rate of 0.02, an average depreciation rate of 0.03 and that θ = 0.5. (a) Reduce the production function to the form y = ak. What is a? (b) What are the growth rates of output and capital in this model? (c) Interpret a. What are we really saying when we assume that the labour-augmenting technology, A, is proportional to the level of capital per worker? (d) What makes this an endogenous growth model?

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Rahul Sunny answered 1 year ago

Suppose that the production function for the economy is Y = AK0.25L0.75, A = 2, K...

Suppose that the production function for the economy is Y = AK0.25L0.75, A = 2, K = 100,000, and L = 60,000. What are the values of real GDP, the real wage, and the real rental cost of capital? Show this data using graphs of the aggregate production function, the aggregate capital market, and the aggregate labor market. Really need help on this ASAP!!

Suppose that output (Y ) in an economy is given by the following aggregate production function:...

Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows at rate...

Suppose that output (Y ) in an economy is given by the following aggregate production function:...

Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows at rate...

Consider an economy with the following production function: Y = K1/2N1/2. The economy has 1,000 units...

Consider an economy with the following production function: Y = K1/2N1/2. The economy has 1,000 units of capital and 1,000 workers. a) Derive the labor demand curve for this economy, (Recall that the real wage, w = MPN. This can be used to solve for N as a function of the other variables). b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage rate? c) Suppose that Congress, concerned about the...

Consider an economy in which the production function is given by Y = 6K1/2N1/2.(a) Derive the...

Consider an economy in which the production function is given by Y = 6K1/2N1/2.(a) Derive the per-worker production function: Y/N = f(K/N). (Hint: A short-cut to get the per-worker production function is to keep the constant, write the ratio (K/N) and then raise the ratio by the same exponent on capital (K).Assume that the depreciation rate is 15% per year and the savings rate is 10% per year.(a) Solve for the steady-state level of capital per worker (K/N).(b) Solve for...

Consider the economy described by the production function Y = F (K, L x E) =...

Consider the economy described by the production function Y = F (K, L x E) = Kα(LE)1-α (a) Derive per effective worker production function. (b) Assume there is population growth rate, depreciation rate and technology growth rate. -Write the law of motion of k. -Tell how k* will be changed when population growth rate increases with graph. (c) Calculate steady state equilibrium. k∗ = y∗ = c∗ = (d) Calculate gold rule capital stock and output. kgold = ygold =...

Suppose an economy is characterized by the following production function: Y = 3K^0.1L^ 0.9 Assume the...

Suppose an economy is characterized by the following production function: Y = 3K^0.1L^ 0.9 Assume the saving rate is 10%, the depreciation rate is 3% and the population growth rate is 2%. a) Find the per worker production function, steady-state capital per worker and output per worker. b) Find steady-state consumption per worker, investment per worker, and saving per worker. c) Briefly explain what would happen to steady-state values of output per worker, capital per worker, and consumption per worker...

An economy has the production function Y=0.4(K+N). In the current period, K=100 and N=100. Graph the...

An economy has the production function Y=0.4(K+N). In the current period, K=100 and N=100. Graph the relationship between output and capital, holding labor constant at its current value. What is the MPK? Graph the relationship between output and labor, holding capital constant at its current value. Find the MPN for an increase of labor from 100 to 110. Compare this result with the MPN for an increase in labor from 200 to 210.

1. Suppose that an economy’s production function is given by Y=10K^(1/3)L^(2/3). The firms in the economy...

1. Suppose that an economy’s production function is given by Y=10K^(1/3)L^(2/3). The firms in the economy are competitive and factors are paid their marginal products. a. Show that the real wage is proportional to average labor productivity. b. Show that the production function satisfies the Euler’s theorem.

Problem 2 Consider an economy described by the production function: Y = F(K,L) = K 1/2...

Problem 2 Consider an economy described by the production function: Y = F(K,L) = K 1/2 L 1/2 a. What is the per- worker production function? b. Assuming no population growth or technological progress, find the steady- state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. c. Assume that the depreciation rate is 10 percent per year. Make a table showing steady-state capital per worker, output...

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Consider an economy whose production function is Y = Kθ(AN)1–θ with A = 4K/N. Suppose that...

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Suppose that the production function for the economy is Y = AK0.25L0.75, A = 2, K...

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