Question

A utility maximizing consumer has a utility function given by \(U(X,Y)=2X+Y\). He has a budget constraint given by \(X+2Y=10\). In equilibrium he purchases:

• A. X=10,Y=10
• B. X=0,Y=5
• C. X=10,Y=0
• D. X=5,Y=5

Hint:

Solve budget constraint and utility function simultaneously

Answer 1

The Correct Option is C

For utility maximization, the budget constraint \(X+2Y=10\) is applied. Solving it yields \(Y=0\) and \(X=10\), satisfying both the utility function and the budget constraint. Therefore, (c) is the correct answer.