Answer to Question #65781 in Microeconomics for Anna

Question

The following utility function marks the preferences over two goods;
U(X1,X2)=X1X2+2X1
There is no budget constraint (income is unlimited)
the prices of the two goods are p1=6 and p2 =8

A) What are the optimal quantities of each given good?

Answer 1

U(X1,X2)=X1X2+2X1
There is no budget constraint, p1=6 and p2 =8
A) What are the optimal quantities of each given good?
If no budget constraint, quantity of each good bought is decided by: Price = Marginal Utility, P = MU.
MU(X1) = U'(X1) = X2 + 2 = p1, so:
X2 + 2 = 6,
X2 = 4.
MU(X2) = U'(X2) = X1 = p2, so:
X1 = 8.