QUESTION 1

A consumer has 40 dollars. The price of x is 5 dollars, and the price of y is 5 dollars. A seller wants to boost the sales of x by giving the consumer a coupon. Coupon $A$ is "buy 4 get 2 for free (can be used for only once)". Coupon $B$ is "20% off". Both coupons are only for purchasing x.

(a) Write down the three budget constraint equations: (1) no coupons, (2) Coupon A, and (3) Coupon B.

(b) Draw the budget constraint lines of three equations.

(c) Suppose the consumer has a utility function: U(x,y) = min{kx, y}. For what values of k, does Coupon A boost sales more than Coupon B?