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 capital.

c) does the economy have more or less capital than at the Golden Rule steady state? how do you know? To achieve the golden rule steady state, does the saving rate need to increase or decrease?

d) suppose the change in the saving rate you described in part c occurs. during the transition to the golden rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part a? after the economy reaches its new steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part a? explain your answers.

Expert Solution

Rahul Sunny answered 7 months ago

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...

An economy has a Cobb–Douglas production function: Y=K^α(LE)^1-α The economy has a capital share of 0.35,...

An economy has a Cobb–Douglas production function: Y=K^α(LE)^1-α The economy has a capital share of 0.35, a saving rate of 43 percent, a depreciation rate of 3.50 percent, a rate of population growth of 3.50 percent, and a rate of labor-augmenting technological change of 2.5 percent. It is in steady state. a.) Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. K*=? y*=? marginal product of capital= ?

An economy has the following Cobb-Douglas production function: Y = Ka(LE)1-a The economy has a capital...

An economy has the following Cobb-Douglas production function: Y = Ka(LE)1-a 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. What is the steady-state growth rate in total output? b. What is the steady-state growth rate in output per worker? c. What is the steady-state growth rate...

Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the...

Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among workers). Markets for output and factors of production are both competitive. The production function is Y = K^1/3*L^1/3*H^1/3 1. Prove that this technology shows constant returns to scale. 2. Solve the competitive firm’s profit maximization problem by deriving the first-order conditions. 3. An...

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...

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 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 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...

1. The output of an economy is characterized by a Cobb-Douglas production function with constant return...

1. The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2. a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium. b). Is a government policy that raises...

Question