A consumer’s utility function is U(x, y) = 2xy2 . The price of x is Px, theprice of y is Py, and the consumer’s income is I. (x and y do not have to be integers.)a) Derive the equation of the consumer’s demand curve for x.b) With y on the vertical axis and x on the horizontal axis, draw a price-consumptioncurve when the price of x changes.c) Suppose the consumer has income I = 150 and faces prices Px = 5 and Py = 10.What is the optimal basket? Calculate the income and substitution effects (withrespect to x) when Px increases to 8.