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Problem 4 Consider the production model in chapter 4. Assume that, in the production function, the...
3. The production function for an economy can be expressed as Y FKL), where Y is...
3. The production function for an economy can be expressed as Y FKL), where Y is real GDP, K is the quantity of capital in the economy, and L is the quantity of labor in the economy If F( ) = 100 + 3K+9L, what is real GDP if the quantity of capital is 200 and the quantity of labor is 500? b. What is/are the endogenous variable(s) in this model? c. What is/are the exogenous variable(s) in this model?
Exercise 1. Production function model Consider an economy "I" with a representative household that consists of...
Exercise 1. Production function model Consider an economy "I" with a representative household that consists of 1000 workers and owns $100 million of capital (L 1000, K -100). There is a representative firm with a Cobb- Douglas production function that rents capital and hires labor to produce. Assume that the TFP parameter equals one (A-1), we have Y K1/3L2/3. Markets are competitive. 1. Define an equilibrium in this economy. Follow class notes. 2. Solve for the equilibrium. You should get...
1. Consider the following production functions. In each case determine if: • the function is Cobb...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
4) Solow Model problem: depreciates at the rate Model problem: A country's production function is Y...
4) Solow Model problem: depreciates at the rate Model problem: A country's production function is Y = K12L12. If capital at the rate of 6% (8 = 0.06) each year, the population grows at the rate of 2% (n ear, and the residents of this country save 36% of income (o = 0.36), solve for the steady-state value of capital per worker (k*), output per worker (y*), and = 0.02) each year, and the reside consumption per worker (c*): C...
Consider the Solow growth model. The production function is given by Y = K αN1−α ,...
Consider the Solow growth model. The production function is given by Y = K αN1−α , with α = 1/3. Depreciation rate δ = 0.05, and saving rate s = 0.25. Labor force grows at the rate n = 0.01. (a) Write down the law of motion for capital per worker. (b) Compute steady state capital per worker. (c) Suppose the economy has initial capital per worker k0 = 4. Describe the dynamics of this economy, i.e., how does capital...
Question 2. In this problem, we will consider how the rental price of capital Rt and...
Question 2. In this problem, we will consider how the rental price of capital Rt and the wage rate we are determined under the assumptions of the Solow growth model. Suppose there exists a representative firm in this economy with Cobb-Douglas production function given by Y = K L-, and that the price of its output P has been normalized to 1. a) Write out the firm's profit function. (Hint: think about what total revenues and total costs are if...
4. Country A is located on a small island that is isolated from the outside world....
4. Country A is located on a small island that is isolated from the outside world. The country has one representative consumer, whose preference is represented by: U (c, l) = ln(c) + ln(l) There is one representative firm in the economy which is owned by the consumer, it produces one type of good that can be used for consumption or government expenditure using capital and labour as inputs. The firm owns the capital it uses and it’s production technology...
1. Suppose the production function in an economy is Y- of capital and L is the...
1. Suppose the production function in an economy is Y- of capital and L is the amount of labor. The economy begins with 8I units of capital and 16 units of labor. a. Suppose also, that one more unit of labor is added to the production process every year for the next four years. What is the marginal product of labor for each year? b. Now, suppose the wage paid per hour is $1.13, the rental price of capital is...
4. Country A is located on a small island that is isolated from the outside world....
4. Country A is located on a small island that is isolated from the outside world. The country has one representative consumer, whose preference is represented by: U (c, l) = ln(c) + ln(l) There is one representative firm in the economy which is owned by the consumer, it produces one type of good that can be used for consumption or government expenditure using capital and labour as inputs. The firm owns the capital it uses and it’s production technology...
3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow...
3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow Model, with usual definitions. Suppose, the labor force is growing at 1% a year, depreciation rate is 4%, and saving rate is 20%. (Total 17 points) a)- Find the steady state equilibrium of per worker levels of capital, output, and consumption. (4) b)- Find the golden rule saving rate, and golden rule per worker levels of output, capital, and consumption. (4) c)- How much...
3. The production function for an economy can be expressed as Y FKL), where Y is real GDP, K is the quantity of capital in the economy, and L is the quantity of labor in the economy If F( ) = 100 + 3K+9L, what is real GDP if the quantity of capital is 200 and the quantity of labor is 500? b. What is/are the endogenous variable(s) in this model? c. What is/are the exogenous variable(s) in this model?
Exercise 1. Production function model Consider an economy "I" with a representative household that consists of 1000 workers and owns $100 million of capital (L 1000, K -100). There is a representative firm with a Cobb- Douglas production function that rents capital and hires labor to produce. Assume that the TFP parameter equals one (A-1), we have Y K1/3L2/3. Markets are competitive. 1. Define an equilibrium in this economy. Follow class notes. 2. Solve for the equilibrium. You should get...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
4) Solow Model problem: depreciates at the rate Model problem: A country's production function is Y = K12L12. If capital at the rate of 6% (8 = 0.06) each year, the population grows at the rate of 2% (n ear, and the residents of this country save 36% of income (o = 0.36), solve for the steady-state value of capital per worker (k*), output per worker (y*), and = 0.02) each year, and the reside consumption per worker (c*): C...
Question 2. In this problem, we will consider how the rental price of capital Rt and the wage rate we are determined under the assumptions of the Solow growth model. Suppose there exists a representative firm in this economy with Cobb-Douglas production function given by Y = K L-, and that the price of its output P has been normalized to 1. a) Write out the firm's profit function. (Hint: think about what total revenues and total costs are if...
1. Suppose the production function in an economy is Y- of capital and L is the amount of labor. The economy begins with 8I units of capital and 16 units of labor. a. Suppose also, that one more unit of labor is added to the production process every year for the next four years. What is the marginal product of labor for each year? b. Now, suppose the wage paid per hour is $1.13, the rental price of capital is...
3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow Model, with usual definitions. Suppose, the labor force is growing at 1% a year, depreciation rate is 4%, and saving rate is 20%. (Total 17 points) a)- Find the steady state equilibrium of per worker levels of capital, output, and consumption. (4) b)- Find the golden rule saving rate, and golden rule per worker levels of output, capital, and consumption. (4) c)- How much...
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