1 Suppose that Cathy consumes two goods beef b and cabbage c

1. Suppose that Cathy consumes two goods: beef (b) and cabbage (c). Her utility function is Ubcs. The price of beef is $9/lb and the price of cabbage is $3/lb. Cathy has S72 (a) What is Cathy\'s MRSb,c for any value of b and c? (b) What is Cathy\'s budget constraint? (c) What is Cathy\'s optimal consumption bundle?

Solution

(a) The mrs is given by the ratio of the two marginal utilities. Thus we have mUb = 1/3*b^-(2/3)*c^(2/3). We have mUc = 2/3c(-1/3)*b^(1/3). Thus the mrs is the ratio of these 2. This c/2b.

(b) The budget constraint is given by 9b + 3c = 72. Which is 3b + c = 24.

(c) The best consumption bundle is solving these 2 together.