Question

In: Economics

Consider a closed economy in which the depreciation rate is 10% per year, the rate of...

Consider a closed economy in which the depreciation rate is 10% per year, the rate of population increase is 2% per year, the rate of technological progress is 1% per year Andy the households save 30% of their income. Suppose the aggregate production function is; Y=f(K, AL)= 9K^4/5 (AL)^1/5 Where Y is output, K is capital, A is the level of technology and L is labor input.

a) Derive the production function in per effective worker terms.

b) Solve for the steady-state values of capital per effective worker (k*), output per effective worker (y*), consumption per effective worker (c*), and savings per effective worker (s*).

c) Derive the equation for the growth rate of output per worker, the growth rate of capital per worker, the growth rate of output and growth rate of capital. What are the values of the growth rates derived?

Solutions

Expert Solution


Related Solutions

Consider a closed economy in which the population grows at the rate of 1% per year....
Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is y = 6 * ((K)^0.5), where y is output per worker and k is capital per worker. The depreciation rate of capital d is 14% per year. a. Households consume 90% of income and save the remaining 10% of income. There is no government. What are the steady-state values of capital per worker, output per worker, consumption per worker,...
Consider a closed economy with no government, a fixed price level, a fixed interest rate and...
Consider a closed economy with no government, a fixed price level, a fixed interest rate and the following characteristics: Autonomous part of consumption expenditure = $10B Investment = $30B Equilibrium GDP = $200B a.  What is autonomous expenditure at equilibrium? (2) b. What is induced expenditure at equilibrium? (2) Now suppose that investment increases to $50B. c. What is the new level of Equilibrium GDP? (2) d. What is the value of the multiplier? (2) e.  Briefly explain the process of convergence...
Consider the Solow model for an economy with a population growth rate of 4%, a depreciation...
Consider the Solow model for an economy with a population growth rate of 4%, a depreciation rate of 12%, a savings rate of 20%, and a production function of Y=5K1/2N1/2 What would the golden-rule savings rate be? Explain what the golden-rule savings rate achieves. Explain what policymakers can do in order to achieve the golden-rule savings rate.
Consider an imaginary economy that has been growing at a rate of 4% per year. Government...
Consider an imaginary economy that has been growing at a rate of 4% per year. Government economists have proposed a number of policies to increase the growth rate but first need to convince the President that the policies will pay off. To do so, they want to present a comparison of the number of years it will take for the economy to double, depending on the growth rate. According to the rule of 70, determine the number of years it...
Consider an imaginary economy that has been growing at a rate of 3% per year. Government...
Consider an imaginary economy that has been growing at a rate of 3% per year. Government economists have proposed a number of policies to increase the growth rate but first need to convince the president that the policies will pay off. To do so, they want to present a comparison of the number of years it will take for the economy to double, depending on the growth rate. Using the rule of 70, determine the number of years it will...
For a closed economy – i.e. an economy in which there are no international transactions –...
For a closed economy – i.e. an economy in which there are no international transactions – GDP is $12 trillion, consumption is $7 trillion, taxes are $3 trillion, and the government runs a deficit of $1 trillion. (Assume transfer payments are zero.) a) It follows that private saving is ________. b) National saving is __________.
Q1. Solow Growth Model. (10 marks) Consider the production function for a closed economy ? =2...
Q1. Solow Growth Model. Consider the production function for a closed economy ? =2 ∙ K1/2(AN)1/2 Assume that the savings rate s equals 20% and the depreciation rate ? equals 5%. Further, assume the growth rate of the labor force gN is 3% and the growth rate of technological progress gA is 2% per year. a. Find the steady-state values of (i) capital per effective worker, (ii) output per effective worker, (iii) the growth rate of output per effective worker,...
suppose private saving in a closed economy is $12 billion and investment is $10 billion. Which...
suppose private saving in a closed economy is $12 billion and investment is $10 billion. Which of the following are true? A. national saving must equal $12 billion B. public saving must equal $2 billion C. Government budget surplus must equal $2 billion D. Government budget deficit must equal $ 2 billion
Consider a bond paying a coupon rate of 10% per year, compounded annually. Assume that the...
Consider a bond paying a coupon rate of 10% per year, compounded annually. Assume that the market interest rate (YTM or return on investments of like risk) is 15% per year. In other words you want a 15% return on the bond.   The bond has three years until maturity. The par value is $1,000. Assume that you buy the bond today for $885.84. 20)   What is the interest payment that you will receive each year (yr 1, yr 2, and...
Consider a bond paying a coupon rate of 10% per year, compounded annually. Assume that the...
Consider a bond paying a coupon rate of 10% per year, compounded annually. Assume that the market interest rate (YTM or return on investments of like risk) is 15% per year. In other words you want a 15% return on the bond.   The bond has three years until maturity. The par value is $1,000. Assume that you buy the bond today for $885.84. 21)   What is the cash flow (interest only) that you want to receive each year (yr 1,...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT