Problems

1.Homer is a street person whose preferences over the two goods he consumes, food (good 1) and fortified wine (good 2) are represented by the utility function U(x₁,x₂)=x₁x₂⁸ (MU₁=x₂⁸, and MU₂=8x₁x₂⁷).Homer receives a pension of $100.00 per week.He can buy food at the local dispensary at a price of $4 a bucket.The local convenience store sells fortified wine at $6 a gallon jug.

a.What is Homer's MRS?

b.Assuming that Homer stays sober long enough to maximize preferences, what are Homer's consumption levels of food and wine?