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.

Expert Solution

Rahul Sunny answered 2 years 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 an economy has the following per-worker production function: y = f(k) = 6...

Suppose an economy has the following per-worker production function: y = f(k) = 6 k1/2 The saving rate is s = .25 = 25%; The depreciation rate is d = .15 = 15%. The initial per worker capital stock (capital-labor ratio) is k = 16. There is no population growth rate. What is the steady state per worker capital stock or capital-labor ratio (k*), k* = ______ per worker output (y*), y*...

An economy has a cobb-douglas production function: Y=K^(a)(LE)^(1-a) The economy has a capital share of 1/3,...

An economy has a cobb-douglas production function: Y=K^(a)(LE)^(1-a) The economy has a capital share of 1/3, a saving rate of 24%, a depreciation rate of 3%, and a rate of population growth of 2%, and a rate of labor-augmenting technological change of 1%. It is in steady state. a) At what rates do total output, output per worker, and output per effective worker grow? b) solve for capital per effective worker, output per effective worker, and the marginal product of...

Let the production function for an economy be Y=AK1/2L1/2 where Y is output, K is capital,...

Let the production function for an economy be Y=AK1/2L1/2 where Y is output, K is capital, L is labor and A is "ideas." If A=4, L=100, the savings rate is 1/5 and the depreciation rate is 1/3, find the steady-state levels of capital, output and consumption. [Answers are all whole numbers.] K*= Y*= C*=

The production function is f(K,N) = N/2 + √ K, where N is the amount of...

The production function is f(K,N) = N/2 + √ K, where N is the amount of labor used and K the amount of capital used. (a) What is returns to scale of this production function? What is the marginal product of labor? (b) In the short run, K¯ = 4. Labor is variable. On the graph, draw output as a function of labor input in the short run in blue. Draw the marginal product of labor as a function of...

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 =...

An economy has a Cobb-Douglas production function: Y=K^α(LE)^1-α The economy has a capital share of 1/3,...

An economy has a Cobb-Douglas production function: Y=K^α(LE)^1-α The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in steady state. A. At what rates do total output, output per worker, and output per effective worker grow? B. Solve for capital per effective worker, output per effective worker, and the...

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

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Suppose that the production function is ? = ? ? in an economy, when K is...

Suppose that the production function is ? = ? ? in an economy, when K is capital and L is labour. What fractions of income do capital and labour receive? Explain your answer. How much is economic profit? Explain your answer.

Consider the following aggregate production function: Y=100×L×K, where A is the total factor productivity, K is...

Consider the following aggregate production function: Y=100×L×K, where A is the total factor productivity, K is the amount of capital in the economy, L is the labour force, and Y is the GDP. Is this aggregate production function exhibiting the constant returns to scale? Explain how you know. (2) Is this aggregate production function exhibiting the diminishing marginal product of capital? Explain how you know. (2) In 1867, the government employed 6% of the country’s workers. Since then, the country’s...

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