A goal of the consumer is to maximize utility.

a. if the budget constraint is M=P1X1+P2X2 show graphically and explain the unique bundle that will maximize utility given the consumer's tastes. Explain why this bundle is unique and optimal. Inlcude in your answer a mathematical explanation describing the equilibrium condition for utility maximization.

b. If the consumer's income falls, explain and show graphically any adjustments that will be made in the consumer's purchases of X1 and X2. Compare the mathematical expression describing the utility maximizing bundle at the two levels of income.

c. On separate diagrams, plot the income-consumption curves for X1 and X2. Explain why each has the particular shape drawn.