Sally Consumes Two Goods, X and Y

Essay

Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3 ∙ XY². The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500.
a. Sketch a set of two indifference curves for Sally in her consumption of X and Y.
b. Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope.
c. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. Show her optimum point on a graph. (Partial units for the quantities are possible.) (Note: MU_Y = 6XY and MU_X = 3Y².)
d. Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What would happen to her utility as a result of the price increase?