Question

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.​)

Answer 1

Answer:

She consumes 30 blue ray disk and 60 DVD respectively.

Step-by-step 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:

$\frac{MU_x}{MU_y}=\frac{P_x}{P_y}$

Substitute the respective values.

$\frac{20xy}{10x^2}=\frac{40}{10}$

$\frac{2y}{x}=4$

$2y=4x$

$y=2x$

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.