(1) [20 points] A consumer with income I = 3 has utility function U(r) = log($1) + 12. [Note: here log(x) denotes the natural logarithm of r in base e.] (a) Find the Marshallian demand. Initially prices are po = (1,1). Let ro = (x, x2) = D(po, I) and uo = V(po, I). Assume the price of good 1 increases so that the new prices are p' = (2, 1). Let x] = 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