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b) Kt+,-4k + (1-8)K, , where q, is the health of the financial system In the...
10 POINTS. Consider the two-period firm optimization problem. Suppose that the only factor of production is...
10 POINTS. Consider the two-period firm optimization problem. Suppose that the only factor of production is capital (no labor is used in production). The production function is y-zK" in the current period and y'-z'K'? in the future period, where z, z, and K are given exogenously and the parameter ? < 1. Real profits are ?-y-1 in the current period and ?-y, + (1- d)K'in the future period. The firm seeks to maximize the present value of lifetime discounted profits,...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Consider a Diamond model, where we set the productivity factor At to unity (1) in all periods. Th...
Consider a Diamond model, where we set the productivity factor At to unity (1) in all periods. The working population. Lt, grows at rate n, i.e., Lt+1-(1 + n) Lt. Lower-case letters denote per-worker terms, e.g earned (from labor) in the first period of life (wi) is spent on saving (St) and first-period consumption (C1t). The first-period budget constraint can thus be written Ki/Lt. Agents live for two perioo In retirement, the same agent consumes C2t+1, consisting of savings from...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and bo...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and both wage and interest rates are equal to one, so that war- a) Given that the wage increases to 4. determine the elasticity of demand for labour at the new wage. Indicate whether the wage bill will increase or decrease as wage increases to 6. b) Find the linear demand function for labour...
1. Consider a firm's production function is given by, F(K,L) al bK, where a and b...
1. Consider a firm's production function is given by, F(K,L) al bK, where a and b are constants. Wage and rent are given by w and r, respectively. Discuss with necessary diagrams, the firm's optimal choice of capital and labor when, i. > (4 points) її. a 14 points) aw b aWw a W ㄑㄧ (4 points)
1. Let's review the setup of the Solow growth model with saving rate s, constant population...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
1. Let's review the setup of the Solow growth model with saving rate s, constant population...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
The Cobb-Douglas production function is given as: Q = AK1-aLa Where 0<a<1, a = .8, K...
The Cobb-Douglas production function is given as: Q = AK1-aLa Where 0<a<1, a = .8, K =4 is the amount of capital, and L=16 is the number of unit of labor, and A = 12 is the measure of TECHNOLOGY INDEX a) Find the real wage of labor (marginal product of labor), W/P, (b) Find rate of return of capital (marginal product of capital), and (c) Discuss the insights of your findings. (d) Why is there not a large amount...
10 POINTS. Consider the two-period firm optimization problem. Suppose that the only factor of production is capital (no labor is used in production). The production function is y-zK" in the current period and y'-z'K'? in the future period, where z, z, and K are given exogenously and the parameter ? < 1. Real profits are ?-y-1 in the current period and ?-y, + (1- d)K'in the future period. The firm seeks to maximize the present value of lifetime discounted profits,...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Consider a Diamond model, where we set the productivity factor At to unity (1) in all periods. The working population. Lt, grows at rate n, i.e., Lt+1-(1 + n) Lt. Lower-case letters denote per-worker terms, e.g earned (from labor) in the first period of life (wi) is spent on saving (St) and first-period consumption (C1t). The first-period budget constraint can thus be written Ki/Lt. Agents live for two perioo In retirement, the same agent consumes C2t+1, consisting of savings from...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and both wage and interest rates are equal to one, so that war- a) Given that the wage increases to 4. determine the elasticity of demand for labour at the new wage. Indicate whether the wage bill will increase or decrease as wage increases to 6. b) Find the linear demand function for labour...
1. Consider a firm's production function is given by, F(K,L) al bK, where a and b are constants. Wage and rent are given by w and r, respectively. Discuss with necessary diagrams, the firm's optimal choice of capital and labor when, i. > (4 points) її. a 14 points) aw b aWw a W ㄑㄧ (4 points)
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
1. Let's review the setup of the Solow growth model with saving rate s, constant population growth rate n, and constant technology growth rate g Kt+1(1-8)K Lt+ 1 = (1 + n) Et+1-(1+g)E a) b) c) What is the steady-state capital and output per effective worker? (5pts) Solve for the golden rule level of capital. What is the saving rate then? (5pts) Many health experts have argued that malnutrition leads to reduced work capacity. Suppose in the Solow model, this...
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