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

Question

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.

Robert · Accepted Answer

Assume that there are two goods in the economy, X and Y. Preferences of consumerA are 
represented by the utility function: Ua=5Q ax (Qay), associated to a marginal rate of substitution 
(MRS) equal to Qay/Qax. . Preferences of consumerB are represented by the utility function: Ub
=Qbx(Qby-100) associated to a marginal rate of substitution (MRS) equal to (Qby-100)/Qbx. Bo
th consumers have an income of $300, and the prices of X and Y are $60 and $2 respectively.  
a) Find (algebraically) consumer’sA utility maximizing (optimal) combination of Qax and Qay. 
At this point compute the level of utility enjoyed by consumer A. 
Answer: 
Budget constraint of consumer A: 60Qax + 2Qay = 300  ……. (1) 
At the utility maximizing point; 
MRS for A = price of x/price of y i.e. 
Qay/Qax = 60/2 = 30,

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...

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