(1) [20 points] A consumer with income I : 3 has utility function U(:r-) : log(:r1) +19. [Notez here log(;r) denotes the natural logarithm of :r in base 6.] (a) Find the l\\-'Iarshallian demand. Initially prices are p0 : (1.1). Let 1:0 : (13?.3'3) : D(p0.I) and a0 : VQJUJ). Assume the price of good 1 increases so that the new prices are p1 : (2.1). Let r1 : D(p1,I) and 111 : V(pl.I). (b) Find the Hicksian demand h(p1,uo). \"that are the income and substitution eects associated with this price change. Draw a picture1 including the indierence curves Uh?) : u0 and Um?) : ul, clearly showing these two eects. (c) Compute the compensating variation (CV) associated with this price change. (d) Draw the demand curve for :1:1 (with :1:1 in the horizontal axis and p1 in the vertical axis) when p2 : 1 and I : 3 are xed. Explicitly compute the change in consumer surplus (ACTS) associated with the price change (you need to nd the numerical value; showing AC8 in the picture is not enough.) (e) Suppose that after prices increase to p1, the consumer is given |ACS| in additional income so that his new income is I0 : I + IACSL What is the consumer's optimal consumption bundle? \"That is his optimal utility