Economic - Utility maximization

Assume that there are two goods in the economy, Xand Y. Preferences of consumerAare

represented by the utility function: Ua=5Q ax (Qay), associated to a marginal rate of substitution

(MRS) equal to Qay/Qax. . Preferences of consumerBare represented by the utility function: Ub=Qbx(Qby-100)associated to a marginal rate of substitution (MRS) equal to (Qby-100)/Qbx. Both consumers have an income of $300, and the prices of X and Y are $60 and $2 respectively.

a) Find (algebraically) consumer’sAutility maximizing (optimal) combination of Qax and Qay. At this point compute the level of utility enjoyed by consumer A.

b) Find (algebraically) consumer's B utility maximizing (optimal) combination of Qbx and Qby. At this point, compute the level of utility enjoyed by consumer B.

c)The price of X is reduced from $60 to $40. Find (algebraically) the newconsumer's A utility maximizing (optimal) combination of Qax and Qay.

d)The price of X is reduced from $60 to $40. Find(algebraically) the new consumer's B utility maximizing (optimal) combination of Qbx and Qby.