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Please solve all the parts.Thank you. A consumer can spend her income on two products, good...

Please solve all the parts.Thank you.

A consumer can spend her income on two products, good X and good Y . The consumer’s tastes are represented by the utility function U(x, y) = xy.

a. Suppose that Px = 4 and Py = 1, and I = 16. Draw the budget line and mark it as BL1. Initial optimum is at A. Find the optimal amounts, xA and yA and locate A on the graph. Find the initial level of utility UA = U(xA, yA).

b. Now suppose Px decreases to P 0 x = 1. Draw the new budget line with the new price and mark it as BL2. Locate the new optimum, C. Find the optimal amounts of x and y at C (xC and yC).

c. Draw the intermediate budget line that yields the initial level of utility under new prices and mark it as BLINT . (BLINT must be tangent to the initial indifference curve, i.e. UA = UB.) Locate point B, the new optimum on BLINT . Find xB and yB.

d. Find the substitution effect and the income effect resulting from this change in Px.

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