5. Determine in the following scenarios whether the good in question is a normal good for sure, an inferior good for sure, or whether one cannot tell from the information given. (a) When Alex was a graduate student with very low income at Boston U, he always ate burritos from a food truck for lunch. Now Alex has graduated and has a well-paying job in Toronto, where burritos from food trucks are cheaper than they were in Boston. Alex eats far fewer burritos now even though he has just as much time for lunch, his preferences haven't changed, the burritos are just as good and the lunch alternatives are more or less the same. For Alex, what kind of good are food truck burritos?(b) In fact, Leo's preferences can be represented by the utility function u(1, ry) = 4vr + 12. The price for nuts is $1 per unit and the price for berries is $2 per unit. Leo has $24 to spend on the two goods. Write down Leo's budget constraint and solve for his optimal consumption bundle.(b) In his grad student days, Alex hardly ever bought himself a lemonade, let alone buying lemonade for others. Now, when he comes back to visit Boston, it's quite possible to see him buy entire rounds of lemonades, even for strangers. The price of lemonade in Boston has not changed, nor have Alex's preferences. For Alex, what kind of good is lemonade?Problem 7 (Signaling) Consider Spence's signalling model. A worker's type is t c (0, 1). The probability that any worker is of type t = 1 is equal to 2/3. while the probability that t = 0 is equal to 1/3. The productivity of a worker in a job is (t + 1)'. Each worker chooses a level of education e 2 0. The total cost of obtaining education level e is C(elt) = e' (2 - t). The worker's wage is equal to his expected productivity. 1. Find pooling equilibrium education levels. 2. Find separating equilibrium education levels. Problem 8 (Moral Hazard) Consider the Principal-Agent model discussed in the slides. Suppose that the effort exerted by the agent can take one of three values ec {1/3,2/3). Also suppose that the Agent's preferences are given by u(w, e) = 2w/2 -e. Leisure yields to the Agent a reservation utility y = 1. The principal's problem can have one of two outcomes: success or failure {7,q}. The payoffs to the Principal in these two events are: 7 = 4 if the outcome is a success and q = 0 if the outcome is a failure. The probability of a success is: pig = 1/3 if the Agent chooses the low effort; and py = 2/3 if the agent chooses the high effort. 1. Let effort be observable. Compute the full-information wages at each effort level. What is the profit maximizing effort for the Principal? 2. Now suppose that the Principal cannot observe effort. For each effort level find output dependent wages that induce the Agent to exert such an effort. 3. Which effort level maximizes the profits of the principal if he cannot observe effort? Which wage schedule should he set to induce the agent to exert such effort.3. Leo consumes only goods 1 and 2. Their prices are p, and pa, respectively, and we let p = (p1, p2). Leo's income is m. His utility function is a(r) = vri + 12. (a) Suppose p1 = 1. Find the general form of his demand functions r- (1, py, m) and of (1, pa, m), which solve the problem2 Leo's birthday is coming 11p and all he has in his pomeaion is one bottle of soda His friends get together and decide to buy him a gift. They agree on getting him some bottles of soda {3} and some fancy colorful soda making powderfshalter contraptions {I}. Leo's utility function is given by UsJ} = s+ fa f2. The soda costs p, = 1 and the powder shaker contraptions cost pf = '2. His friends decide to buy him two bottles of soda {in addition to the one he already has} and one powder shaker thing, spending a total of $4. {Throughout this question, you can assume that both soda and the fancy powder things can he consumed in any fractional amount. When drawing diagrams, put soda on the horizontal axis and the powder shaker things on the vertical aids. Also, you should only he coneerned about the negatively sloped portions of the indierence curves. Do not worry about portions which are positively sloped.) {a} At Leo's initial position prior to receiving the gifts, is he optimized