Problem 3 Consumer\'s Choice of Recorded Music versus Concerts (): In 2011, a ty

Question

Problem 3 Consumer's Choice of Recorded Music versus Concerts (): In 2011, a typical American music buyer, Jackie, spent about S140 per year on music, among which 40% was spent on recorded music and 60% on concerts. (X-Recorded Music; Y Concert) 1) Define an appropriate uility function to represent Jackie's consumption behavior. (4 points) 2) Calculate MRSxy. Does MRSxy diminish as X increases? (2 points) 3) Suppose the average price of recorded music was Px-$8 per album, and the average price of concert was Py S20. How many recorded music and concerts did Jackie purchase in 2011 in order to maximize his satisfaction? (4 points) 4) At the optimal consumption level, calculate the values of MRSxy. Verify that MRSxy Px/Py. (2 points) 5) Suppose the average price of recorded music increased to PxA-$10 per album, and the average price of concert stayed same Py $20. How many recorded music and concerts would Jackie have purchased in 2011 in order to maximize his satisfaction? Again verify that at the optimal solution, MRSxy MUxMUy Px/Py. 6) Suppose the average price of recorded music dropped to PxB S6 per album, while the average price of concert stayed same Py $20. How many recorded music and concerts would Jackie have purchased in 2011 in order to maximize his satisfaction? Did MRSxy MUx/MUy Px/Pyl hold at the optimal solution? 6) Plot the three different budget lines in part 2), part 4), and part 6) due to changes in prices of recorded music, show the intercepts; Plot the indifference curves and show the optimal solutions in part 2), part 4 and part 6)

Explanation / Answer

Answer

a)

As consumer is spending fix proportion of income on both goods. This must be a cobb douglas function. Let Recorded music be represented by X and concert by Y.

U = XaYb

As he is spending 40% of Income on Recorded

Then a/(a+b) = 0.4

and He is spending 60% on Concert

We have b/(a+b) = 0.6

Solving this we get a =2 and b=3

U = X2Y3

b)

MRS = MUx/MUy

= 2XY*3/3X^2Y^2 = (2/3)*(Y/X)

Hence MRS will decrease as Y/X decrease with increase in X

c)

U = X2Y3

As it is a cobb douglas,

Optimum quantity of X is given by (2/(2+3))*M/Px

Optimum quantity of Y is given by (3/(2+3))*M/PY

M = 140 ,PX = 8, PY = 20

Putting these values above We get

So Quantity of X = 7  

and Quantity of Y = 4.2 ~ 4

d)

MRS = (2/3)*(Y/X) =  (2/3)*(4.2/7) = 0.4

Px/Py = 8/20 =0.4

Hence Px/Py = MRS

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.