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.)
Accepted Solution
A:
Answer:She consumes 30 blue ray disk and 60 DVD respectively.Step-by-step explanation:Consider the provided information.[tex]U(x,y)=10x^2y[/tex]Calculate marginal utility of goodDifferentiate with respect of x and y.[tex]MU_x=20xy[/tex][tex]MU_y=10x^2[/tex]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:[tex]\frac{MU_x}{MU_y}=\frac{P_x}{P_y}[/tex]Substitute the respective values.[tex]\frac{20xy}{10x^2}=\frac{40}{10}[/tex][tex]\frac{2y}{x}=4[/tex][tex]2y=4x[/tex][tex]y=2x[/tex]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, [tex]40x+10y=1800[/tex][tex]4x+y=180[/tex]Substitute the value of y in above equation.[tex]4x+2x=180[/tex][tex]6x=180[/tex][tex]x=30[/tex]Thus, [tex]y=60[/tex]She consumes 30 blue ray disk and 60 DVD respectively.