Question

A consumer’s utility function over goods X and Y is U(X,Y)=XY + 10Y. Suppose this

consumer has an income of $110, the price of good Y is $2, and the price of good X

is $1. What is the optimal consumption bundle (X*,Y*) for this consumer?

Answer 1

$X+ 2\cdot Y = 110$ and $X\cdot Y + 10\cdot Y = 0$ , than connect them and get formula $(110-2y)\cdot Y + 10\cdot Y = 0$ After solving it we have, that y = 50, than put it in one of the formula and get x = 10