2. Consumer problem, homothetic preferences, demand. Assume preferences for food (f) and cloth (c) are described by the following Cobb-Douglas utility function: U(xc, *f) = x2 (1) where a E (0,1). Denote by po, pfthe prices of the two goods, and by / a consumer's income. (a) Solve the maximization problem, ie., compute the optimal consumption values as functions of prices and income.1 (b) Compute the expenditure share in each of the good, defined by$, = 1, for j = af. Interpret your findings. (c) Compute relative demand: xc*/* expressed as a function of pc/pf. Cobb-Douglas preferences are homothetic: does relative demand depend on income