Questions: A university is trying to raise funds to build a state of arts auditorium. Total cost to build the auditorium will be $5 million. The university has identified two possible donors for the project. Let S1 and S2 denote the donations of Donor 1 and 2, respectively. Question 1: Donor 1's utility from donating S1 is (1/2) (S1 + S2) - S1. Donor 2's utility from donating S2 is (1/4) (S1+S2) - S2. The two donors simultaneously decide how much to donate (or equivalently, Donor 1 does not know Donor 2's donation amount, while deciding how much to donate, and vice-versa.) 1. lot the Best Response functions of the Donors. Plot S1 along the x - axis and plot S2 along the y - axis. Properly label your diagram. 2. Find out the Nash equilibrium amount of donations for each donor. If there are multiple Nash equilibria, find out all of them. Justify your answer. Question 2: Now, suppose that the university identifies a third donor. Donor 3 will donate $3 million if S1 + S2 at least $2…

Two 657 students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by Ui(fi, xi) = 0;(fi)+xi, where ø:(·) is strictly concave, f; is the amount of food consumed by student i, and x; is a composite numeraire good. Each student has a fixed budget of m;. EVALUATE THIS CLAIM: Both students eat too much!

Market research revealed that the customers can be separated into 5 groups according to their preferences over bundles of goodxs x and y. The respective empirical utility functions were constructed and they look as follows: 1. U1(x,y) = 2x+5y. 2. U2(x,y) = 100/(2x+5y). 3. U3(x,y) = 3(2x+5y)0.5 4. U4(x.y) = 7(2x+5y)². 5. U5(x,y) = -150/(2x+5y). How many different preferences were identified by the market research. O 1 O 3

Vhee Ayar lives alone in a computer lab where it spends 10 hours per day producing spurious orside calls (denoted xf) and awarding incomprehensible penalties (denoted xp). Vhee Ayar can conjure 8 offside calls per hour, and it can summon 6 penalties per hour. The utility that Vhee Ayar derives from offside calls and penalties is captured by the utility function U(Xf, xp) = 3xf x05. How many offside calls and penalty kicks will Vhee Ayar choose to produce/consume each day?

Consider two friends Anna and Elsa whose gains and losses are listed as follows: Anna's investment is worth $2.5 million (decreased from $3.5 to $2.5 million) Elsa's investment is worth $2.2 million (increased from $2 to $2.2 million) For each of them write down the reference utility function (First determine the reference point (use a parameter) and derive reference utility function for each).

Consider a consumer with the utility function U (x1, x2 ) = 10x12/3x21/3 −50. Suppose the prices of x1 and x2 are 10 and 2 respectively and the consumer has an income of 150. (a)  Write out the consumer’s constrained optimization problem. Specifically, write out the objective function and constraint for the problem (e.g. max _?_ subject to _?__). (b)  Write the Lagrangian equation corresponding to the constrained optimization problem. Derive the Necessary First Order Conditions. (c)  Use the NFOCs to solve for the consumer’s optimal bundle. (d)  Show that at the solution you found in (c), the tangency condition is satisfied: MRS = p1 / p2. (e)  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 change if the utility function was x12x2? Lastly, how would…

A consumer has the following utility function (shown in image) where ? is the number of spa days and ? is the number of city breaks consumed. Suppose that the price of a spa day is £200 and the price of a city break is £300. (i) Set up the economic problem and find the numbers of spa days and city breaks that minimise expenditure if 12,800 units of utility are to be obtained.

Beans and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and donuts (K). Utility function of the consumer is the following: U(B,K) = 100∙B^0.25 · K^0.75 The price of beans (can) is ISK 2,000. but the price of a donut (box) is ISK 4,000. Consumption restrictions are placed on the consumer since his income is ISK 400,000. Put on all form donuts on the x-axis and beans on the y-axis. a) Show an equation for the bean's success rate for a single donut in light of the utility function. Draw the equivalence curve on a picture and explain what the equation is performance ratio is stated at each point on the equivalence curve. Explain with the concept of the efficiency ratio of the curvature of the equivalent curve. b) Find the most efficient consumption combination and draw on the diagram. c) The government decides to support the consumption of beans so its price drops to 1,000. Who is the most economical consumption combination based on the changed price…

Marbella has 101 residents. All wear the same fancy clothes and each has the same utility function, u(m, b, B) = m + 14b − b2 − B/50, where m is the amount of macaroni (in kilograms) that he or she eats per day, b is the number of hours that he or she spends on the beach per day, and B is the total number of person-hours spent per day on the beach by other residents of Marbella. Each has an income of $10 per day and macaroni costs $1 per kilogram. The city council is considering a law that would limit the amount of time that any person can spend on the beach. How many hours per day should they allow in order to maximize the utility of a typical Marbellite? A. 6 B. 9 C. 7 D. 10 E. They could not possibly be made better off by legislation that limits their freedom to choose.