MATH SOLVE

5 months ago

Q:
# Given the following Demand Curve: P = 24 - 8QExpress this Demand Curve in terms of Q.Use either the original equation or the one in part (a) and find P if Q=2.Use either the original equation or the one in part (a) and find Q if P = 8.Write out the equation for total revenue in terms of Q.Write out the equation for marginal revenue in terms of Q. Hint: Marginal revenue is the first derivative of total revenuFind the values of P and Q that will maximize total revenue.Calculate this maximum value of total revenue.

Accepted Solution

A:

Answer:Maximum value of total revenue = 18Step-by-step explanation:Express this Demand Curve in terms of Q.P = 24 - 8Q (it is the same equation)Find P, if Q=2P= 24-8(2)P=24-16P=8Find Q if P = 8.P = 24 - 8Q8= 24 - 8Q8Q= 24-88Q=16Q=16/8Q=2Total revenue in terms of QTotal revenue is P times Q, that isP*Q=TR=(24-8Q)*QTR=24Q-8Q^2[tex]TR=24Q-8Q^{2} \\\\[/tex]Marginal RevenueIt is the first derivative of TRTR'(Q)= 24-16QFind the values of P and Q that will maximize total revenue.To find them first TR'(Q)=0, that is0=24-16Q16Q=24Q=24/16Q=3/2Q=1.5and we plug in 1.5 in P=24-8Q, which is,P=24-8QP=24-8(1,5)P=24-12P=12Calculate this maximum value of total revenueP=12 Q=1.5P*Q=Total Revenue12*1.5=Total Revenue18=Total Revenue