Beyonce receives utility from consuming healthy food F and f

Beyonce receives utility from consuming healthy food (F) and fabulous clothing (C) as given by the utility function U(F, C) = (FC). In addition, the price of healthy food is $4 per unit, the price of fabulous lothing is $40 per unit, and Beyonce\'s weekly income is $100,000.

Solution

(a) MRS = MU(F) / MU(C)

Utility is maximized when MRS equals the price ratio.

So, MRS = PF / PC = 4 / 40 = 0.10

(b) MRS of food for clothing indicates the number of units of clothing that Beyonce will give up to obtain 1 additional unit of food.

If she is consuming more of healthy food and less of clothing, then she will be willing to give up more units of food to obtain 1 unit of clothing, or equivalently, less units of clothing to obtain 1 unit of food. So, MRS will be lower than 0.1.