Question

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)=XjX28 (MUi=x2", and

MU2=8xıx27). 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.

What is Homer's MRS?

Answer 1

$Given:\\ U=x_1x2^8\\ MU_1=x2^8\\ MU_2=8x_1x_2^7\\ MRS_{12}=\frac{MU_1}{MU_2}\\ MRS_{12}=\frac{x_2^8}{8x_1x_2^7}\\ MRS_{12}=\frac{x_0^2}{8x_1}\\ So, Homer's MRS is \frac{x_2}{8x_1}$