Answer to Question #251119 in Microeconomics for Raman

Question

The consumer has set a budget of $M for the consumer of good X and Y .The price of good X is $Px and the price of good Y is $py.The consumer has a utility function given by U(X,Y)=xy^2.
Find the optimal consumtpion choice of the individual and the ulitlity obtained.
Make a graph that illustrates the solution to the problem.

Answer 1

Budget=$M

Utility function:

$U(X,Y)=xy^2$

Budget constraint:

$P_XX+P_YY=M$

The optimal consumption choice is the consumption choice that maximizes the consumer's total utility given his/her budget constraint.

Optimal choice$=\frac{MU_X}{MU_Y}=\frac{P_X}{P_Y}$

At the optimal consumption choice, the slope of the indifference curve equals the slope of the budget line.