Economics True or False. Please provide a short explanation. A person with the utility function U(x, y) = y1/3 + x1/2 has well-behaved preferences.
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- You have $4,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and theprice 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?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?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.
- Another instance when people are likely not to spend a dime (or a minute) on an item is when they have a dislike for mixing the item with other items available. In this case, we say the consumer has ‘non-convex preferences’ and indifference curves are bowed out from the origin. In plain language, the consumer has a preference for binging. We often feel this way towards our favorite social media app. Consider a kid who has four hours a day to spend on social media. They enjoy spending time on Snapchat (x) or spending time on Twitter (y). a) Write the kid’s time constraint and illustrate it in a graph where you measure time spent on Snapchat along the horizontal axis and time spent on Twitter along the vertical axis. This kid’s utility from time spent on Snapchat and time spent on Twitter is U(x,y) = 4x2+ y2. b) In your graph, draw a couple of the kid’s indifference curves. Notice how the kid’s |MRSY,X| increases along each curve as he spends more time on Snapchat and less time on…Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’s satisfaction. If price of Banana is increased by $.25, what will be the new combination of A and B that would maximize her utility? Show graphically and drive the demand curve for BananasGiven a Utility function: U(x,y) = 3xy. Suppose the Price of x is 2, and the price of y is 4. What is the optimal choice of y as a function of x. ( MRS = (Px/Py).
- Suppose a consumer’s preferences can be represented by the utility function U(X,Y) = Min (2X,Y). Also, suppose the consumer has $300 to spend and the price of Good X is PX = $2 and the price of Good Y is PY = $5. If the consumer maximizes their utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase? X* = Y* =.Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S,T) = 2ST, so MUs = 2T and MUT = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on shoes and dancing. A. What is the equation for her budget line? Draw it (with T on the vertical axis) and label the slope and intercepts. B. What is Linda's marginal rate of substitution? Explain. C. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line.True or false. Maximizing choices occur when combinations of two goods are made such that they are affordable and achieve the highest indifference curve (i.e. the highest utility).
- Joyce consumes x1 and x2 together in fixed proportions. She always consumes 1 unit of x2 for 2 units of x1. What is the utility function that describes her preference?Consider the following scenario: Ahmad dislikes plain coffee, unless he eats something sweetie with the coffee. In particular, he likes to consume Starbuck's coffee (X2) only if he is compensated by one caramel doughnut (X,) while drinking the plain coffee. Otherwise, drinking plain coffee is not desirable for him. Ahmad has budget M, Ahmad's target utility is U = K, the marginal utility of one doughnut is A, and his marginal disutility of one plain coffee without doughnut is “– B". A. Write down Ahmaď's consumer optimization (objective and constraints). B. Derive Ahmad's demand functions for plain coffee (X2) and doughnuts (X,). C. What is Ahmad's maximum utility? D. Get the compensation inequality condition. E. Find the minimum compensation required for Ahmad to consume Starbuck's plain coffee. F. Show graphically.Consider the following utility function: U(x,y)= min{x+2y, 2x+y}. If a person’s income is $100 and px=$10, py=$20, then find out the quantity of x and y that will maximize utility.
