Create an inverse demand of P = a – bQ, inverse demand of P = 11 – 2Q. a) Calcul
ID: 1229791 • Letter: C
Question
Create an inverse demand of P = a – bQ, inverse demand of P = 11 – 2Q.a) Calculate the marginal revenue (MR).
b) Find the quantity and price which maximize profits when marginal cost is zero (round off to two decimal places for any number that is not a whole number).
c) What is the revenue generated by this price and quantity?
d) At that price and quantity, what is the consumer surplus (CS)?
e) Find the price elasticity of demand at that quantity.
f) If the quantity is restricted to be no greater than Q’ = 3.00, what does this do to the firm’s revenue? If Q represents the number of seats sold, and Q’ represents the seating capacity of the stadium, would your stadium have empty seats?
Please show work so i can understand how you got the answers, i need to be able to learn this on my own.
Thanks very much
Explanation / Answer
a) Calculate the marginal revenue (MR). TR=P*Q =(11-2Q)Q =11Q-2Q^2 MR=derivative of TR =11-4Q b) Find the quantity and price which maximize profits when marginal cost is zero (round off to two decimal places for any number that is not a whole number). Set MR=0 since MR=MC at this point set equal to zero 11-4Q=0 4Q=11 Q=11/4 P=11-2(11/4) P=44/4-22/4=22/4=6 c) What is the revenue generated by this price and quantity? TR=6*11/4=66/4=33/2=16.5 d) At that price and quantity, what is the consumer surplus (CS)? 1/2(6-0)(11/4-0)=33/4=8.25 e) Find the price elasticity of demand at that quantity. (11/4-0)/(0-6)= -.458 f) If the quantity is restricted to be no greater than Q’ = 3.00, what does this do to the firm’s revenue? This will cause demand to be much higher than supply and leave a shortage. There will be a social loss or dead weight loss to society. The firms revenue will decrease. If Q represents the number of seats sold, and Q’ represents the seating capacity of the stadium, would your stadium have empty seats? In this case, or stadium would sell out and have no empty seats becasue the new price is less than the price at equilibrium Hope this helsp
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