An individual values two goods, X and Y, according to the following utility function: U (X,Y)= 6 (0.5 X-0.88 +0.5 Y-0.88)-1.14 The price of X is Pr-4, and the price of Y is Py-4. The individual has 16 dollars. How much X and Y should this individual buy? (Round answers to the nearest two decimals. For example, 1.666 rounds to 1.67.) X Number Y Number

Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1. Find this family’s monthly food expenditure.The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8)

The following five individuals have different utility functions over food (good x) and clothing (good y): 1) u₁(x, y) = 3x²y 2) u₂(x, y) = 2√x + y 3) Uz(x, y) = x0.6y0.4 4) u₁(x, y) = x² + y² 1 5) us(x, y) = x + 3y For each of these people: a) Compute their marginal utilities of good x, MUx = Ju(x,y) MU, = ду du(x,y) ax b) Check whether the property of "more is better" is satisfied for both goods? Explain. [Hint: Check whether marginal utilities are positive assuming positive amounts of good x and good y] ƏMUX əx and marginal utility of good y, c) Does the marginal utility of good x diminish, remain constant, or increase as each of the individuals buys more x? Explain. [Hint: There are 2 ways to do it: 1) visually check what happens to the expression of MUx when x increases (does it decrease, keep constant or decrease?); or 2) take the partial derivative of this marginal utility with respect to x, that is ƏMUx .aMUX ƏMUX If 0, the marginal utility of x is increasing in x] d) Does the…

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Kai spends his income on lime (L) and ginger water (G). Lime is priced at $2, while ginger water costs $1. Suppose Kai has $30 to spend and his utility function can be represented as U(L,G) = L0.5 G0.5 What is the optimal number of lime and ginger water for Kai to purchase? b. How much utility does this combination bring him?

Anton, Betsy and Catherine are three college friends who regularly go the movies. At the movies, they can purchase skittles (x) and junior mints (y). The table below display the total utility each of them get from bundles of these two snacks (x, y). Bundle A = (1,1) B = (1,2) C = (1,3) D = (1,4) E = (1,5) Anton's Anton's Utility MUY (2) (1) 10 14 16 17 17.5 Betsy's Utility (3) 10 10 9 8 7 Betsy's MU, (4) Catherine's Utility (5) 10 12 15 19 24 Catherine's MUY (6) a) Yesterday the three friends went to watch the Barbie movie and they purchased the same bundle, bundle B = (1,2), with 1 bag of skittles and 2 bags of junior mints. Can you say who of the three friends experienced the highest utility from consuming bundle B? Explain. b) As you may have noticed, all bundles in the table contain 1 bag of skittles while they differ in the number of bags of junior mints. Fill in columns (2), (4) and (6) in the table by computing the marginal utility each friend receives from choosing a bundle…

Suppose that a consumer has the utility function U(X,Y)= 2X 1/2 y 1/2 for X>0 and Y> 0. Which of the following utility functions would not represent the same preferences? U(X,Y)= 2(X + Y) 1/2 U(X,Y)=2x1/2y 1/2 - 100 O U(X,Y)= In 2 + InX+ In Y O U(X,Y)= X 1/2 y 1/2 O U(X, Y) = 4XY

Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.

Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y   Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).

2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂