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5. A consumer has the utility function U= In C+In (24-N), where C is consump- tion...
need help on b, c and d please. 2. Suppose a consumer has the utility function...
need help on b, c and d please.
2. Suppose a consumer has the utility function over goods x and y u(x,y) = 4x^y (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x*(Papy,m) and y" (Px.py,m). Show all of your work...
Problem 3: Inelastic labor supply A representative consumer has preferences described by the utility function: u(c)...
Problem 3: Inelastic labor supply A representative consumer has preferences described by the utility function: u(c) = ln c, where c denotes consumption. Assume that the total number of hours available to the worker are h¯ = 1. The consumer/worker receives the wage, w, for her labor services. A. Obtain the labor supply curve. B. Introduce a proportional tax on labor income, τw. Obtain the new labor supply curve. C. Introduce a proportional tax on consumption, τc. Obtain the new...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
3. Micheal has a utility function of the following: U(L, X) = Lº X1-a, where L...
3. Micheal has a utility function of the following: U(L, X) = Lº X1-a, where L is leisure and X is consumption. If he works, he receives real wage w. Outside of the labor market, he has non-labor market income V. And his endowment of time T is normalized to 1. And the price of goods p is also normalized to 1. (a) Please write down his budget constraint. (b) Assuming a = Į, V = 100, w = 200,...
1. CRRA Utility Function: Constant relative risk aversion, or CRRA, utility function has been extensively used...
1. CRRA Utility Function: Constant relative risk aversion, or CRRA, utility function has been extensively used in macroeconomic analysis to represent consumer behavior. It takes the following general form u(x)- where σ is known as the curvature parameter. For the remainder of this question assume that σ>0. Assume that a representative household in a one-period model has the following preferences over consumption and leisure where l is leisure. The budget constraint is (in nominal terms) Pc nominal wage and n...
1. Suppose a consumer has the utility function over goods x and y u(x, y) =...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
Suppose that all agents in the economy have the following utility function U(c,l)=( c(1-θ) /(1- θ...
Suppose that all agents in the economy have the following utility function U(c,l)=( c(1-θ) /(1- θ ))-l where c is consumption, l is the supply of labor, and θ a fixed parameter. Suppose that individuals only have labor income, with an hourly wage of w and a tax rate of t. Thus, the budget constraint of the agent is w(1-t) l=c . We will assume here that θ = 0.5 and w = 1. The elasticity of the labor supply with...
A representative consumer has preferences described by the utility function: uc, 1) = ln(c- c) +...
A representative consumer has preferences described by the utility function: uc, 1) = ln(c- c) + Inl where c denotes consumption and I leisure. The parameter o captures the level of subsistence consumption. Assume that the total number of hours available to the worker are h = 1. The consumer/worker receives the wage, w, for her labor services. A. Obtain the labor supply curve. B. Introduce a proportional tax on labor income, T. Obtain the new labor supply curve. C....
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c)...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c) + Bln(c'), where B is a parameter between 0 and 1, and assume that there is always an interior solution to the household's problem. 12. What is the marginal rate of substitution of current consumption for future con- sumption MRS given this utility function? How does it change with c and c'? 13. Solve the household's optimization problem with the lifetime budget constraint. That...
need help on b, c and d please.
2. Suppose a consumer has the utility function over goods x and y u(x,y) = 4x^y (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x*(Papy,m) and y" (Px.py,m). Show all of your work...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
3. Micheal has a utility function of the following: U(L, X) = Lº X1-a, where L is leisure and X is consumption. If he works, he receives real wage w. Outside of the labor market, he has non-labor market income V. And his endowment of time T is normalized to 1. And the price of goods p is also normalized to 1. (a) Please write down his budget constraint. (b) Assuming a = Į, V = 100, w = 200,...
1. CRRA Utility Function: Constant relative risk aversion, or CRRA, utility function has been extensively used in macroeconomic analysis to represent consumer behavior. It takes the following general form u(x)- where σ is known as the curvature parameter. For the remainder of this question assume that σ>0. Assume that a representative household in a one-period model has the following preferences over consumption and leisure where l is leisure. The budget constraint is (in nominal terms) Pc nominal wage and n...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
A representative consumer has preferences described by the utility function: uc, 1) = ln(c- c) + Inl where c denotes consumption and I leisure. The parameter o captures the level of subsistence consumption. Assume that the total number of hours available to the worker are h = 1. The consumer/worker receives the wage, w, for her labor services. A. Obtain the labor supply curve. B. Introduce a proportional tax on labor income, T. Obtain the new labor supply curve. C....
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c) + Bln(c'), where B is a parameter between 0 and 1, and assume that there is always an interior solution to the household's problem. 12. What is the marginal rate of substitution of current consumption for future con- sumption MRS given this utility function? How does it change with c and c'? 13. Solve the household's optimization problem with the lifetime budget constraint. That...
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