Q1. Consider a consumer with a lifetime utility function U(c, c') = u(c) + Bu(c) that satisfies all the standard assumptions listed in the book. The period 1 and 2 budget constraints are c+s=y c+sy+(1+r)s (a) What is the optimal value of s'? Impose this optimal value and derive the life-time budget constraint.
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- You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?Find the quantities of each product that the consumer should buy, subject to the budget, that will allow maximum satisfaction. That is, find values of x and y that maximize U = f(x,y), subject to xpy + ypy = 1. Assume that such a maximum exists. U=x°y°: Px =2, py = 3, 1 = 60 (x³y³ + o) The values that maximize U are x = and y = (Simplify your answers.)Q- Marginal utility can never be negative. True/False
- Find Indirect utility function of the following function U = max (X, Y) subject to the budget constraint P, X+ P₂ Y=M Optionis O O max (P1 P2) M² min (P1 P2) M² P1+ P2 M min (P1 P2)Ann's utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2 and Y.QUESTION 1 For the utility function U = Qx0.50Qy(1-0.50) and the budget 122 = 8Qx + 14Qy find the CHANGE in optimal consumption of Y if the price of Xincreases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).
- For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +XbEXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…of 55 The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume
- Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.Assume that you have a budget of Taka 4000 that can spend on two goods like: coke and burger. Suppose coke costs Taka 100 per unit and burger costs 400 per unit. Suppose also that your utility function is given by the equation U(B, C) = 20BC. Write your budget equation. What combination of coke and burger should you buy to maximize utility?Adrienne consumes three goods, x, y, and z. Her consumption preference is given by the utility function: u(x, y, z) = x*y} z#, (Pz-Py, Pz) where x, y, and z are the quantities she consumes (respectively). Let p = be the prices of the goods. Answer the following questions, and justify your answers carefully and mathematically. (a) Last year p = sumption bundle last year. (1, 10, 10) and Adrienne's income was 35. Find her optimal con- (b) This year, the prices of x and z have both risen 3.5% while the price of y has risen 7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage changes of her consumption in the three goods due to these changes in prices and income. Does her raise adequately compensate her for the changed prices? What additional percentage change of her income would be needed if we were to restore Adrienne to last year's exact utility level?