Consider a consumer that maximizes a utility function of the form: U = 10 X.3 Y.7[Note: you do not need to use Lagrangian]

a) If the Price of Good X is $9 and the Price of Good Y is $7, what is the minimum cost for this consumer to achieve utility U = 20? For parts b) to d), the consumer has income of $100 and the Price of Good Y is $7/unit.

b) Please write the equation for the demand curve for Good X (Q as a function of P).

c) How much will this consumer demand of Good X when the price of Good X is $9/unit?

d) Consider that the preferences of the consumer change to U = 10 10 X.5 Y.5 and that the price of Good X is still $9/unit. Please show how this change affects BOTH the Indifference Curve/Budget Constraint diagram and the Demand Curve diagram for Good X. Label the equations of ALL curves (Budget Constraint, Indifference Curves, and Demand Curve for Good X) and any key points including the initial optimum and the final optimum in both diagrams.10 points - Calculation of new optimum 10 points - IC/BC diagram 5 points - Demand diagram