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car ​as the following utility​ function: ​U(X,Y)equals10Upper X squaredY where X is her consumption of​ Blu-ray disks with a price of ​$40 and Y is her consumption of DVDs with a price of ​$10. She has ​$1800 with which to spend on the two goods. Determine the number of​ Blu-ray disks and DVDs that will maximize Cary​'s utility. Cary maximizes utility when she consumes nothing ​Blu-ray disks and nothing DVDs. ​(Enter your responses using integers.​)

User Dong Chen
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1 Answer

4 votes

Answer:

She consumes 30 blue ray disk and 60 DVD respectively.

Explanation:

Consider the provided information.


U(x,y)=10x^2y

Calculate marginal utility of good

Differentiate with respect of x and y.


MU_x=20xy


MU_y=10x^2

Her consumption of​ Blu-ray disks (X) with a price of ​$40 and Y is her consumption of DVDs with a price of ​$10.

The ratio of marginal utility of good x to y is equal to the price ratio:


(MU_x)/(MU_y)=(P_x)/(P_y)

Substitute the respective values.


(20xy)/(10x^2)=(40)/(10)


(2y)/(x)=4


2y=4x


y=2x

She has ​$1800 with which to spend on the two goods.

Her consumption of​ Blu-ray disks (X) with a price of ​$40 and Y is her consumption of DVDs with a price of ​$10. She has ​$1800 with which to spend on the two goods.

Therefore,
40x+10y=1800


4x+y=180

Substitute the value of y in above equation.


4x+2x=180


6x=180


x=30

Thus,
y=60

She consumes 30 blue ray disk and 60 DVD respectively.

User Spencer Cole
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