Maurice has the following utility function UX Y 20X80YX22Y2

Maurice has the following utility function: U(X, Y) = 20X+80Y-X^2-2Y^2 Where X is his consumption of CDs with a price of $1 and Y is his consumption of movie videos with a rental price of $2. He plans to spend $41 on both forms of entertainment. Determine the marginal utility of increasing consumption of X, keeping consumption of Y constant. Determine the marginal utility of increasing consumption of y, keeping X constant. Hence, determine the marginal rate of substitution between x and y. What is Maurice\'s budget constraint? What is the slope of his budget constraint? Determine the number of CDs and video rentals that will maximize Maurice\'s utility.

Solution

MUx =dU/dX(Partial derivative) = 20 - 2X

MUy =dU/dY(Partial derivative) = 80 - 4Y

MRS = MUx/MUy = (20-2X)/(80 - 4Y)

Budget constraint, I =PxX+PyY, 41 = X + 2Y

Slope of budget constraint = -Px/Py = -1/2