1. Richard and Mary Johnson have fallen on hard times but remain rational consumers. They are making do on $100 a week. Food (x) costs $2 per unit. Draw a budget line for the couple on the (x, y) coordinates, where x is food and y is the money for other goods (money is a numeraire, whose price is 1). a. Assume that their utility is U = X^0.5 Y^0.5 .

Figure out the dollar amounts they spend on x and y.

(a) The couple suddenly become eligible for food stamps. This means that they can go to the agency and buy coupons that can be exchanged for $2 worth of food. Each coupon costs them $1. However, the maximum number of coupons they can buy per week is 10. On the graph, draw their new budget line.

(b) How many units of X and Y will they buy once they enter the food stamp program? How many more units of X will they purchase?

(C) If the maximum coupons they can buy increase to c units (where C>10), what will the effect be on their consumption? Characterize the effect in detail as C continues to increase. Obtain the maximum units of coupon they are willing to buy.

2. Percy consumes cakes and ale. His demand function for cakes is q_c = m - 30p_c + 20 p_{a, where m is his income, Pa is the price of ale, Pc is the price of cakes, and qc is his consumption of cakes. Percy's income is $100, and the price of ale is $1 per unit.}

_{(a) Is ale a substitute for cakes or a complement? Explain.}

_{(b) What is an equation for Percy's demand function for cakes where income and the price of ale are held fixed at $100 and $1.}