Homework Answers
The expected utility function is given as:
Thus, the functional form of the expected utility function is:
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Consider the expected utility function U (,)u (z) + Eyu (zs) = miVa+ are...
uppose that a consumer's utility function is U, where x and y are goods and z...
uppose that a consumer's utility function is U, where x and y are goods and z is a bad (e.g. pollution, so that more pollution decreases utility of the consumer). If consumption of x and z is growing at a rate of 2% and 3%, respectively, and that of y declines at 196, what is the growth rate in the utility the consumer derives from that consumption? Use total differentiation and show all your work/steps.
2. Consider an individual whose utility function over income I is U(I), where U is increas-...
2. Consider an individual whose utility function over income I is U(I), where U is increas- ing smoothly in I and is concave (in other words, our basic assumptions throughout this chapter). Let Is be this person's income if he is sick, let 1н be his income if he is healthy, let p be his probability of being sick, let EI be expected income, and let ElU] be his expected utility when he has no insurance. Assum e 0 <...
Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a,...
Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a, b, c are constants. The prices of good x and y is denoted by pX and pY respectively. The income is denoted by m. Good z is provided by the government free of cost but the quantity of good z provided by the government depends on the consumption of good x and y chosen by the consumer. For example, if in equilibrium, the consumer...
Consider the expected utility function 71u (21) + Tzu (22). Let x2 = f (x1, U)...
Consider the expected utility function 71u (21) + Tzu (22). Let x2 = f (x1, U) describe an indifference curve for this utility function, so that hju (x1) + Tzu (f (x1,U)) = U. Differentiate this expression with respect to x1 to find the slope of an indifference curve. Find the slope of this indifference curve when x1 = 22. Explain why it has this slope.
1. This problem asks you to consider the effects of a distortionary tax on consumption. Let utility be given by U = In...
1. This problem asks you to consider the effects of a distortionary tax on consumption. Let utility be given by U = Inc+ ß In c' with budget constraints c(1+t) = yes d' (1+t) = y +s (1+r). (a) Solve the budget constraints for c and d and substitute the resulting expressions into utility, writing utility as a function of s. Maximize utility with respect to s. Write an expression for the Euler equation. (b) Does the distortionary tax affect...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some...
2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some arbitrary good and ơ (the Greek letter "sigma") is known as the "curvature parameter" because its value governs how curved the utility function is and is treated as a constant. In the following, restrict your attention to the region c > 0 (because "negative consumption" is an ill-defined concept) a. (0.50 Points) Plot the utility function for σ 0, Does this utility function display...
Please help me with this question, thank you so much! 1.a) Consider an agent who will...
Please help me with this question, thank
you so much!
1.a) Consider an agent who will live for two periods with utility function U(x1, x2) = x1 * x * . The agent receives incomes 11 and 12 in periods 1 and 2 respectively. If the market interest rate is r = 10% and 14 = $10 and 12 = $10, solve for the agent's optimal consumption in each period. Graph the budget constraint and some indifference curves.
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and...
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and the budget constraint: C - 1+r 1+r where y = 100, y 120, and the interest rate r = 0.05. a) What is the optimal value of current consumption c*? b) What is the optimal value of future consumption, c*? c) Suppose the interest rate r -0.10. What is the new value of optimal current consumption c*? Suppose the new interest rate r =...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z Problem 4 (a) Derive the demand functions for the utility function (b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the...
uppose that a consumer's utility function is U, where x and y are goods and z is a bad (e.g. pollution, so that more pollution decreases utility of the consumer). If consumption of x and z is growing at a rate of 2% and 3%, respectively, and that of y declines at 196, what is the growth rate in the utility the consumer derives from that consumption? Use total differentiation and show all your work/steps.
2. Consider an individual whose utility function over income I is U(I), where U is increas- ing smoothly in I and is concave (in other words, our basic assumptions throughout this chapter). Let Is be this person's income if he is sick, let 1н be his income if he is healthy, let p be his probability of being sick, let EI be expected income, and let ElU] be his expected utility when he has no insurance. Assum e 0 <...
Consider the expected utility function 71u (21) + Tzu (22). Let x2 = f (x1, U) describe an indifference curve for this utility function, so that hju (x1) + Tzu (f (x1,U)) = U. Differentiate this expression with respect to x1 to find the slope of an indifference curve. Find the slope of this indifference curve when x1 = 22. Explain why it has this slope.
1. This problem asks you to consider the effects of a distortionary tax on consumption. Let utility be given by U = Inc+ ß In c' with budget constraints c(1+t) = yes d' (1+t) = y +s (1+r). (a) Solve the budget constraints for c and d and substitute the resulting expressions into utility, writing utility as a function of s. Maximize utility with respect to s. Write an expression for the Euler equation. (b) Does the distortionary tax affect...
Problem 1 Consider a consumer with the utility function U(21,22) = 10x 23 -50. Suppose the prices of X1 and 22 are 10 and 2 respectively and the consumer has an income of 150. How did the '50' in the utility function influence the optimal con- sumption bundle? How did the '10' in the utility function influence the optimal consumption bundle? (i.e., how would the optimal bun- dle change if these coefficients were to change?). How would the optimal bundle...
2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some arbitrary good and ơ (the Greek letter "sigma") is known as the "curvature parameter" because its value governs how curved the utility function is and is treated as a constant. In the following, restrict your attention to the region c > 0 (because "negative consumption" is an ill-defined concept) a. (0.50 Points) Plot the utility function for σ 0, Does this utility function display...
Please help me with this question, thank
you so much!
1.a) Consider an agent who will live for two periods with utility function U(x1, x2) = x1 * x * . The agent receives incomes 11 and 12 in periods 1 and 2 respectively. If the market interest rate is r = 10% and 14 = $10 and 12 = $10, solve for the agent's optimal consumption in each period. Graph the budget constraint and some indifference curves.
3. Suppose you are given the utility function: In c' 4 U=In c +- Ci and the budget constraint: C - 1+r 1+r where y = 100, y 120, and the interest rate r = 0.05. a) What is the optimal value of current consumption c*? b) What is the optimal value of future consumption, c*? c) Suppose the interest rate r -0.10. What is the new value of optimal current consumption c*? Suppose the new interest rate r =...
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