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3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and...
1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг...
1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг and the budget constraint: c+ =yt 1+r 1+r where y = 5, y' = 10, and the interest rate r = 0.10. Now suppose that y=5 again, and there is only one consumer in the entire economy. If we add in government expenditures and taxation, the consumer's budget constraint is now: c+ y' = y + -t- +r 1+r 1+r If current and future...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow is p2. John gets an income of m, today and m2 tomorrow. (a) John also faces the interest rate, r. Write out John's intertemporal budget constraint in present value and future forms. (4 marks) (b) It turns out that John earns an income of £15000 today and...
can anyone help me with this question? 2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consum...
can
anyone help me with this question?
2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income...
1. (12 points) Adapted from Williamson chapter 9 question 1. Jason's income in the current period...
1. (12 points) Adapted from Williamson chapter 9 question 1. Jason's income in the current period is y 2200, and income in the future period is U2-2000. The real interest rate is 4%. (a) (2 points) Suppose that current and future consumptions are perfect comple- ments for Jason His life time utility is given by minsc, c21. Draw Jason's indifference curves (b) (2 points) Jason's indifference curves are not the usually smooth curves. The marginal condition for Jason does not...
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...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also,...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
Question 1 (3 Points): Assume a consumer has current-period income y = 120, future-period income y'...
Question 1 (3 Points): Assume a consumer has current-period income y = 120, future-period income y' = 140, current and future taxes t = 20 and t' = 10, respectively, and faces a market real interest rate of r = 0.08, or 8% per period. The consumer has the following preferences over current and future consumption: U(c, c') = min(4c, 3c'). a) (1 points) Determine the consumer's lifetime wealth. b) (2 points) Determine what the consumer's optimal current-period and future-period...
1. Consider the following two period consumption savings problem. A consumer cares about consumption (c and...
1. Consider the following two period consumption savings problem. A consumer cares about consumption (c and future consumption c according to Assume that U(c) is given by for some constant y. In the present the consumer chooses how much to consume and how much to save out of her income y>0 This decision is made in the knowledge that in the future she will be retired, have no income, and thus future consumption will be entirely out of savings: c)a,...
3. A consumer's preferences over a and y are given by the utility function u(x,y) -...
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
1. Suppose you are given the utility function: VC U = vc + 1.10 CI уг and the budget constraint: c+ =yt 1+r 1+r where y = 5, y' = 10, and the interest rate r = 0.10. Now suppose that y=5 again, and there is only one consumer in the entire economy. If we add in government expenditures and taxation, the consumer's budget constraint is now: c+ y' = y + -t- +r 1+r 1+r If current and future...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow is p2. John gets an income of m, today and m2 tomorrow. (a) John also faces the interest rate, r. Write out John's intertemporal budget constraint in present value and future forms. (4 marks) (b) It turns out that John earns an income of £15000 today and...
can
anyone help me with this question?
2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income...
1. (12 points) Adapted from Williamson chapter 9 question 1. Jason's income in the current period is y 2200, and income in the future period is U2-2000. The real interest rate is 4%. (a) (2 points) Suppose that current and future consumptions are perfect comple- ments for Jason His life time utility is given by minsc, c21. Draw Jason's indifference curves (b) (2 points) Jason's indifference curves are not the usually smooth curves. The marginal condition for Jason does not...
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...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
Question 1 (3 Points): Assume a consumer has current-period income y = 120, future-period income y' = 140, current and future taxes t = 20 and t' = 10, respectively, and faces a market real interest rate of r = 0.08, or 8% per period. The consumer has the following preferences over current and future consumption: U(c, c') = min(4c, 3c'). a) (1 points) Determine the consumer's lifetime wealth. b) (2 points) Determine what the consumer's optimal current-period and future-period...
1. Consider the following two period consumption savings problem. A consumer cares about consumption (c and future consumption c according to Assume that U(c) is given by for some constant y. In the present the consumer chooses how much to consume and how much to save out of her income y>0 This decision is made in the knowledge that in the future she will be retired, have no income, and thus future consumption will be entirely out of savings: c)a,...
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
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