Exchange (Chapter 32 in the book) Problem 3. Consider a small exchange economy with two consumers, Anna and Bob, and two commodities, milk and cookies. Anna's initial endowment is 4 gallons of milk and 1 pound of cookies. Bob's initial endowment is 0 gallons of milk and 7 pounds of cookies. Anna's utility function is UA(mA,cA) = mA :0: cA. Bob's utility function is U3(m3,03) = mjn{m3,03}. m; is the amount of milk in gallons for Anna (1' = A) or Bob (1' = B), and c; is the amount of cookies in pounds for Anna (1' = A) or Bob (3' = B). (a) Draw an Edgeworth box, showing the initial allocation and sketching two indifference curves for each consumer. Measure Anna's consumption from the lower left and Bob's consumption from the upper right. (b) Draw the locus of Pareto optimal allocations (Hint: Check your notes, where we discussed demand function for the min utility function or page 100 in the book. The optimal solution for the min utility function always happens at the kink point). (G) Let the price of milk bep (i.e.pm = p) and let cookies be the numeraire good (i.e. with price pc = 1). What is Bob's demand for milk at these prices? (Hint: Bob's income is Bob's endowment at the given prices). (d) What is the value of Anna's endowment at the prices pm = p and p5 = l? (e) What is Anna's demand for milk at prices (pmpc) = (p,1)? (f) What is the Pareto optimal price vector