Q. Suppose Bailey consumes two things, food (F) and clothing (C), and her preferences are described by the following utility function:

u (F, C) = 10FC

(a) Suppose that Bailey has 10 total items. Given only her preferences, would she prefer to have more food than clothing or more clothing than food? That is, does she like food or clothing better? Explain.

(b) Suppose that Bailey can make her own food and clothing. The feasible frontier that describes how she is able to convert food into clothing can be expressed using the following equation:

25 = F^2 + C^2

Graph her feasible frontier with F on the x-axis.

(c) Interpret the two intercepts of the feasible frontier in words.

(d) How much utility does Bailey get by consuming at the intercepts of the feasible frontier? Explain in words by discussing the shape of her indifference curves.

(e) Find the MRT when Bailey produces 3 units of food.

(f) Find the MRS when Bailey consumes 3 units of food and is ON the feasibility frontier.

(g) Compare the MRT and MRS that you just obtained. In order to get to a higher indifference curve and remain on her feasible frontier, what should Bailey consume more of? Explain.

(h) Suppose instead that Bailey can purchase food for Pf = $5 and clothing for Pc = $10. Given these prices, what is her opportunity cost of food in terms of clothing?

(i) Assume that if Bailey only purchases clothing, she can buy 10 units of clothing. Can you draw the "feasible frontier" based on this intercept and the opportunity cost you found above?

(j) Congrats, you've just drawn a budget constraint! See if you can come up with the equation for the line you just drew.