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Numerical Example: A household's optimization problem Given: household's utility: U(C,e) 15 In l 16 In C...
Numerical Example: Static GE - the social planner Given: household's utility: U(C,) 15 In 16 In...
Numerical Example: Static GE - the social planner Given: household's utility: U(C,) 15 In 16 In C production function: Y 10vKN total time endowment h -9, government spending G 22.5 and capital stock K - Follow these steps: 9 o write down the planner's resource constraint o solve the planner's problem o find the endogenous variables, including C, e, N, Y
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0)...
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the household's indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The household's labour income is therefore wNs, where N-h-l-16- l is the time...
Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9,...
Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9, wage w 7.5 Follow these steps: write down the expression for the firm's profit π o optimize: find the profit-maximizing level of employment find output y and profit π
Consider a two-period economy discussed in Chapter 9. Suppose there are only two households, and each...
Consider a two-period economy discussed in Chapter 9. Suppose there are only two households, and each household's utility function and endowment are given as follows. u' (C1,C2) = (C122) and e' = (18,4). u? (C1,C2) = Incı + 2 Inc and e? = (3,6). el denote the allocation of endowment income for household i. For simplicity, there is no government, and therefore no tax in both periods. There is a perfectly competitive credit (financial market in which they can buy...
Problem 5 Assume that a worker has the Utility Function U(C,L) C "C" refers to consumption in dollars and &...
Problem 5 Assume that a worker has the Utility Function U(C,L) C "C" refers to consumption in dollars and "L" to hours of leisure in a day. The worker has an offered wage of $10 per hour, 20 hours available for leisure or work per day, and $30 dollars a day from non- labour income. o 8.60 L (a) Find the budget constraint equation of the individual. (b) Find the optimal choice for the individual in terms of units of...
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,...
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...
3. (4 p.) Bill's utility function is U = c + l where c is a...
3. (4 p.) Bill's utility function is U = c + l where c is a composite good with price equal to 1 and lis leisure. He earns w per hour and owns C units of the composite good and his time endowment is T. (a) Find his reservation wage. (b) Derive Bill's demand for leisure (ordinary demand), illustrate graphically the resulting demand curve and explain its slope. (c) Assume that C = 0 and real wage rate is 3....
5. A consumer has the utility function U= In C+In (24-N), where C is consump- tion...
5. A consumer has the utility function U= In C+In (24-N), where C is consump- tion and Nis labor supply. Her budget constraint is pC MwN, where p is the price of the consumption good, w the wage rate, and M the consumer's non- wage income. (a) Formulate the problem of utility maximization subject to the budget con- straint, and derive the first-order conditions, using the Lagrange multi- plier approach and ignoring the nonnegativity constraints. 80 1 Static optimization Find...
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100...
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100 hours to divide between work and leisure per week wage is $20/hr 1. Write down budget constraint in terms of consumption and hours of work 2.Tom make decisions on hours of work, leisure and consumption to max. utility. Explain why we can collapse this problem to one in which he chooses hours of leisure only 3. Find optimal hours of work and total consumption...
Numerical Example: Static GE - the social planner Given: household's utility: U(C,) 15 In 16 In C production function: Y 10vKN total time endowment h -9, government spending G 22.5 and capital stock K - Follow these steps: 9 o write down the planner's resource constraint o solve the planner's problem o find the endogenous variables, including C, e, N, Y
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the household's indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The household's labour income is therefore wNs, where N-h-l-16- l is the time...
Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9, wage w 7.5 Follow these steps: write down the expression for the firm's profit π o optimize: find the profit-maximizing level of employment find output y and profit π
Consider a two-period economy discussed in Chapter 9. Suppose there are only two households, and each household's utility function and endowment are given as follows. u' (C1,C2) = (C122) and e' = (18,4). u? (C1,C2) = Incı + 2 Inc and e? = (3,6). el denote the allocation of endowment income for household i. For simplicity, there is no government, and therefore no tax in both periods. There is a perfectly competitive credit (financial market in which they can buy...
Problem 5 Assume that a worker has the Utility Function U(C,L) C "C" refers to consumption in dollars and "L" to hours of leisure in a day. The worker has an offered wage of $10 per hour, 20 hours available for leisure or work per day, and $30 dollars a day from non- labour income. o 8.60 L (a) Find the budget constraint equation of the individual. (b) Find the optimal choice for the individual in terms of units of...
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,...
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...
3. (4 p.) Bill's utility function is U = c + l where c is a composite good with price equal to 1 and lis leisure. He earns w per hour and owns C units of the composite good and his time endowment is T. (a) Find his reservation wage. (b) Derive Bill's demand for leisure (ordinary demand), illustrate graphically the resulting demand curve and explain its slope. (c) Assume that C = 0 and real wage rate is 3....
5. A consumer has the utility function U= In C+In (24-N), where C is consump- tion and Nis labor supply. Her budget constraint is pC MwN, where p is the price of the consumption good, w the wage rate, and M the consumer's non- wage income. (a) Formulate the problem of utility maximization subject to the budget con- straint, and derive the first-order conditions, using the Lagrange multi- plier approach and ignoring the nonnegativity constraints. 80 1 Static optimization Find...
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