# Answer to Question #65781 in Microeconomics for Anna

Question #65781

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?

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?

Expert's answer

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.

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.

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