You have $4,000 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(T, M) = T3/4M1/4. 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?

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).

21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =

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)

1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?

Suppose the total utility function for the consumer who is consuming two goods, good x and good z is U(x, z) = ln(2x) + 2lnz.  The consumer’s income is $16 and is faced with the prices of each unit of good x and good z.  The price per unit of good x is $4 and the price per unit of good z is $1.  How many units of good x and good z should the consumer consume so as to maximize his/her utility?  Also, what will be the total utility earned from the consumption of that many units of good x and good z?

Question 3 (Demand). Carlos really likes pizza. His utility function for Little Caesar's (xi) and Woodstock's (x.) is given by: U(xi, x2) = x;+2x2 The price of x,is $10 and Carlos spends $50 on pizza. a) Graph the demand curve for x1, with pi (the price of x) on the y-axis and x, on the x-axis. (Hint: There will be a range of prices where the demand for x, will be 0). Explain you graph. Page 2

Suppose you have an income of $24 and the only two goods   you consume are apples (x1) and peaches (x2). The price of apples is $4 and the price of peaches is $3. Suppose that your optimal consumption is 4 peaches and 3 apples.   a. Illustrate this in a graph using indifference curves   and budget lines.   b. Now suppose that the price of apples falls to $2 and   I take enough money away from you to make you as happy   as you were originally. Will you buy more or fewer   peaches? Provide a graphical representation.

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Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.