Sylvester and Rachel live together on an island with two goods, food and shelter. Food is a private good and shelter is a public good. The utility function of Sylvester is U= Fs+ 2(Zs+ Zr) where Fs is the amount of food he buys, Zs is the amount of shelter he buys and Zr is the amount of shelter Rachel buys. Similarly, the utility function of Rachel is U= Fr+ Zs+ Zr where Fr is the amount of food she buys. Suppose the price of food is 10 and both Sylvester and Rachel have 100 to spend. Suppose also that it is not possible for Sylvester and Rachel to reach any kind of agreement. a. Determine the quantity of shelter they will buy and the efficient quantity of shelter if the price of shelter is 5? (Enter your answer in whole number.) Quantity of Shelter: Efficient 120 units b. What is the quantity of shelter they will buy if the price of the shelter is 15? (Round your answer Quantity of Shelter: Not Efficient 30 units 2 decimal places (e.g., 32.16).) What is the quantity of shelter they will buy if the price of the shelter is 25? (Enter your answer as a whole number.) Quantity of Shelter: (Click to select) units

Granny lives in the Woods and consumes only bread and fruits. One week she falls ill and has to ask her niece, Red, to buy her weekly food. Red lives in the City, where the price of fruit is $ 2 per kilogram and the price of bread is also $ 2 per loaf. Red knows that Granny's utility function is given by U(f, b) = In (f) + 2 In (b) and that Granny has allocated $ 60 of her income for food each week. Heading to Granny's house in the Woods with the food bought from the City in her basket, Red unexpectedly meets the infamous trader B. B. Wolf, which offers to buy or sell food at a price of $ 3per kilogram of fruits, and $ 6per loaf of bread. Show graphically, what is the Red's budget line before meeting with Wolf and the budghet line after meeting with Wolf?

Problem 1: Exchange economy Consider an exchange economy with two consumers, A and B, and two goods, X and Y. Consumer A has an initial endowment TA = i >0 of good X, an initial endowment yA = 0 of good Y, and preferences over consumption bundles that can be represented by the Cobb-Douglas utility function uA(TA: YA) = ", where ra is the quantity of good X, yYA is the quantity of good Y, and a € (0, 1) is a preference parameter. Consumer B has an initial endowment ig = 0 of good X, an initial endow- ment js = j > 0 of good Y, and preferences over consumption bundles that can be represented by the Cobb-Douglas utility function up(rB, YB): B1-3 where rB is the quantity of good X, YB is the quantity of good Y, and BE (0, 1) is a preference parameter. (a) Find the set of Pareto optimal allocations in this economy. In appro- priate diagrams, illustrate the set of Pareto optimal allocations when (i) 3 = a, (ii) 3 > a, and (iii) 3 a.

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. Consumer A is initially endowed with 10 units of good 1 and 10 units of good 2. Consumer B is initially endowed with 2 units of good 1 and 2 units of good 2. The consumers have the following utility functions: ua(X1a,X2a)=X1AX2A²; uB(x1B,X2B)=X1B+X2g. Among the prices below, which ones are Walrasian equilibrium prices? O a. p1=3, p2 =2 O b. p1=4, P2 =5 O C. None of the other answers. O d. p1=5, p2 =4 O e. P1=2, p2 =3