Maurice has the following utility function: U(X, Y) = 20X+80Y-X^2-2Y^2 Where X i
ID: 1258240 • Letter: M
Question
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.Explanation / Answer
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