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Problem 5: Consider the following variation of the aggregate production function....
Problem 5: Consider the following variation of the aggregate production function. Now firms must use oil...
Problem 5: Consider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The price of a unit of oil is p (a) Find a first-order condition for the firm's demand for oil. (b) What must be true about the parameters α, β, and γ if this production function exhibits constant returns to scale? (c) If the price of oil p rises, what would you expect to...
1. (The AK Model) Consider an economy with an aggregate production function given by y =...
1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital....
Please explain and show all the steps instead of just giving an answer. (Production function) Condsider...
Please explain and show all the steps instead of just giving an
answer.
(Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (i) exhibits positive and diminishing marginal product and (iii) has constant return to scale: 1. Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K,...
Please explain and show all the steps instead of just giving an answer. 1. (Production function)...
Please explain and show all
the steps instead of just giving an answer.
1. (Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) eahibits positive and diminishing marginal product and (ii) has constant return to scale Y F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K.L) -...
1. (Production function) Condsider a representitive firm with a production function which is (i) twice continuously...
1. (Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) exhibits positive and diminishing marginal product and (iii) has constant return to scale: Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit max F(K, L) - RK - wL K,L a) Denote FK , FL=52. Show that...
Please explain and show me the process with answer. Thank you! 1. (The AK Model) Consider...
Please explain and show me the
process with answer. Thank you!
1. (The AK Model) Consider an economy with an aggregate production function given by Y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. T he law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing...
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...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 6K1/3L2/3 In this economy, workers consume 80% of income and save the rest. The labour force is growing at 2% per year while the annual rate of capital depreciation is 5.5%. a) Solve for the steady state capital-labour ratio and consumption per worker. The economy is in its steady state as described in part (a). Suppose both the stock of capital...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
(Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable;...
(Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) exhibits positive and diminishing marginal product and (ii) has constant return to scale: Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K, L) - RK - wL K,L 3. (Solow Model) Denote that Y F(K, L)...
Problem 5: Consider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The price of a unit of oil is p (a) Find a first-order condition for the firm's demand for oil. (b) What must be true about the parameters α, β, and γ if this production function exhibits constant returns to scale? (c) If the price of oil p rises, what would you expect to...
1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital....
Please explain and show all the steps instead of just giving an
answer.
(Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (i) exhibits positive and diminishing marginal product and (iii) has constant return to scale: 1. Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K,...
Please explain and show all
the steps instead of just giving an answer.
1. (Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) eahibits positive and diminishing marginal product and (ii) has constant return to scale Y F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K.L) -...
1. (Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) exhibits positive and diminishing marginal product and (iii) has constant return to scale: Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit max F(K, L) - RK - wL K,L a) Denote FK , FL=52. Show that...
Please explain and show me the
process with answer. Thank you!
1. (The AK Model) Consider an economy with an aggregate production function given by Y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. T he law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing...
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...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
(Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) exhibits positive and diminishing marginal product and (ii) has constant return to scale: Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K, L) - RK - wL K,L 3. (Solow Model) Denote that Y F(K, L)...
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