QUESTION Consider the following Cobb Douglas production function: Y= K2/5L3/5. The rate of depreciation in the...

QUESTION

Consider the following Cobb Douglas production function: Y= K^2/5L^3/5. The rate of depreciation in the economy is 2% and the marginal propensity to save (mps) is 30%. Any output that is not saved is consumed and this is a closed economy. Population growth rate is zero.

Continue with the same data with the exception that mps is unknown. Solve for the rate of investment which will ensure golden rule of consumption per capita . Show all the steps covered in the discussion for the practice problem clearly to avoid grade penalty.

b. Continue with the same data above but introduce the following change. The rate of depreciation changes to 4% for capital per worker greater than or equal to 400. For k<400, the rate of depreciation still continues to be 2%.Use a well labeled graph to show the steady state behaviour in this new scenario. In your answer you must indicate the numerical magnitudes of the associated capital per worker and output worker. Show the steps you have followed to obtain the numerical answers.

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider the following Cobb Douglas production function: Y= K2/5L3/5. The rate of depreciation in the economy...

Consider the following Cobb Douglas production function: Y= K2/5L3/5. The rate of depreciation in the economy is 2% and the marginal propensity to save (mps) is 30%. Any output that is not saved is consumed and this is a closed economy. Population growth rate is zero. 1. Continue with the same data with the exception that mps is unknown. Solve for the rate of investment which will ensure golden rule of consumption per capita 2. Continue with the same data...

Consider an economy with the following Cobb-Douglas production function:

Chapter 7, Labor Market Regulation (3 points):• Consider an economy with the following Cobb-Douglas production function:Y =k^1/3L^2/3The economy has 1,000 units of capital and a labor force of 1,000 workers.(a) Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock (Hint: Review Chapter 3.)(b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and...

Consider an economy with the following Cobb-Douglas production function: Y = K1/3L 2/3 .

Consider an economy with the following Cobb-Douglas production function: Y = K1/3L 2/3 . The economy has 1,000 units of capital and a labor force of 1,000 workers. 1a. Derive an equation describing labor demand as a function of the real wage and the capital stock. (Hint: this is a review from what we did in Chapter 3)b. If the real wage can adjust to equilibrate labor supply and labor demand, what is the resulting equilibrium real wage? In this...

Consider the standard Solow model with saving rate is 30%, and depreciation rate is 5%, Cobb-douglas...

Consider the standard Solow model with saving rate is 30%, and depreciation rate is 5%, Cobb-douglas production function with A = 1, α = 0.3. Suppose initially the economy is at the steady state. If we increase the saving rate from 30% to 50% once for all. Plot the ﬁrst 20 periods of the following after the change: • capital sequence • output sequence • consumption sequence

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time,...

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time, derive the conditional input demands ? ∗ (?, ?, ?) and ? ∗ (?, ?, ?) and the associated long-run cost function ?(?, ?, ?) under the assumption that ? + ? = 1. b) Describe the average cost and marginal cost functions. How do they depend on output q and factor prices w and r? Explain. c) Continuing to assume ? + ?...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...

Consider the Cobb-Douglas production function Y = eb0 K b1 Lb2 eui where Y, K and...

Consider the Cobb-Douglas production function Y = eb0 K b1 Lb2 eui where Y, K and L denote real output, real capital input, and real labor input, respectively. The data for estimating the parameters of the production function are given in the Excel data file productionfunction.xls. Perform a logarithmic transformation of the production function to linearity so that it can be estimated by OLS. Compute the correlation coefficient between income lnK and lnL and comment on the potential for multicollinearity....

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1....

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1. Let ? be the amount of labor, ? the amount of capital, and ? be the amount of other materials used. Let the profit function be defined by ?=?−(??+??+??) where the costs of labor, capital, and other materials are, respectively, ?, ?, and ?. Determine whether second order conditions for profit maximization hold, when the profit function is defined by ?=?−(30?+20?+10?) with ?=5?^0.3?^0.4?^0.2.

Consider the following hypothetical economy. The production function is Cobb-Douglas and labor's share of income is...

Consider the following hypothetical economy. The production function is Cobb-Douglas and labor's share of income is 70%. All values are continuously compounded, annualized growth rates, in percent. Growth in real wages: 2.0 Growth in capital stock: 4.0 Growth in real rental rate of capital: 1.0 a. Using the information provided in the table above, your best estimate of growth in TFP is A. 1.4% B. 2.9% C. Not enough information to answer D. None of the above b. Consider a...

Consider an economy with the following Cobb–Douglas production function: Y=5K1/3L2/3. a. Derive the equation describing labor...

Consider an economy with the following Cobb–Douglas production function: Y=5K1/3L2/3. a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint : Review Chapter 3.) b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage, total output, and the total amount earned by workers. c. Now suppose that Congress, concerned...

Subjects