(1) [20 points] A consumer with income I = 3 has utility function U(x) = log(r1) + 12. [Note: here log(r) denotes the natural logarithm of r in base e.] (a) Find the Marshallian demand. Initially prices are po = (1, 1). Let ro = (rix2) = D(po, I) and uo = V(p', I). Assume the price of good 1 increases so that the new prices are p = (2, 1). Let r = D(p', I) and u1 = V(p', I). (b) Find the Hicksian demand h(p , u). What are the income and substitution effects associated with this price change. Draw a picture, including the indifference curves U(x) = u' and U(x) = u, clearly showing these two effects. (c) Compute the compensating variation (CV) associated with this price change. (d) Draw the demand curve for $1 (with r1 in the horizontal axis and p, in the vertical axis) when p2 = 1 and I = 3 are fixed. Explicitly compute the change in consumer surplus (ACS) associated with the price change (you need to find the numerical value; showing ACS in the picture is not enough.) (e) Suppose that after prices increase to p , the consumer is given |ACS] in additional income so that his new income is / = 1+ (ACS). What is the consumer's optimal consumption bundle? What is his optimal utility