Sara's income is 120 a week. The price of popcorn (PP) is 15 a bag, and the price of cola (PC) is 30 a pack. Sara has the utility function U(P,C)= 5PC. Marginal utilities of popcorn and cola areMUC =5P and MUP =5C.

a)Findthe optimal bundle of Sara (P*,C*). (5points max)

b)Sara is facing two situations(i)her income increases to150 ( withP_P= 15 and P_C= 30)and (ii) the price of Cola decreases (P_P=P_C=15 and her income is 120). What will Sara choose to maximize her satisfaction (we assume that Sara is a rational person)? (10 pointsmax)

(i)Changes in the income

(ii)Changes in the price of Cola

c)Build the Sara's demand line of Cola, that depicts the changes in a demand because the changes in the price (5 pointsmax)

d)What is price elasticity of Cola ? (5 pointsmax)