Please only do C~~E

(1) [20 points] A consumer with income I = 3 has utility function U(x) = log(x1) + 12. Note: here log(x) denotes the natural logarithm of x in base e.] (a) Find the Marshallian demand. Initially prices are p = (1, 1). Let x0 = (x9,x9) = D(p, I) and wo = V(p, I). Assume the price of good 1 increases so that the new prices are pl = (2, 1). Let x = D(p', I) and u1 = V(pl, 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 x1 (with x] in the horizontal axis and p1 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 " - I-+ (ACS|. What is the consumer's optimal consumption bundle? What is his optimal utility