1. Suppose the demand for baseballs is given by: Qd = 450 – 5P where Qd is the q
ID: 1190454 • Letter: 1
Question
1. Suppose the demand for baseballs is given by:
Qd = 450 – 5P where Qd is the quantity demanded of baseballs and P is the price of baseballs.
a) If the price of baseballs is $9, what will be the total revenue collected from the sale of baseballs?
b) What is the Price Elasticity of Demand for baseballs between the prices of $5 and $6 (please give your answer in the form of a fraction)?
c) What is the price elasticity of demand at a price of $24?
d) If the price of baseballs is $24, should the firm raise or lower their price if they want to increase their total revenue.
e) What price should the firm charge if it wants to maximize its revenue?
Explanation / Answer
a) Q = 450-5P; at P = $9 Q will be 450-45 -405, revenue = P*Q = 9*405 = $3645
b) Price ealsticity = (Q2-Q1)*P1/((P2-P1)/Q1) here P1 = 5 now Q1 will be 450-5*5 = 425; similarly P2=6 Q2 will be 450-9*6 = 420 So price elasticity = (420-425)*5/(6-5)*425 = =25/425 = -1/17
c) To find price elasticity of demand i need two prices P1=$24 assume P2 = $25 Q1(at P1) = 450-120 = 330 Q2(at P2) = 450-125 = 325 Price elaticity = -5*24/330 = -4/11
d) Firms can maximize the revenue till elasticity per unit price change approaches to value of -1 Now if we compare b) and c) we see that in c) the elasticity is nearer to -1 in comparision to b) but still not reached -1 so prices can be raised further to maximize the revenue
e)R = Q*P now R = 450P-5P2 so to maximize revenue dR/dP = 0 ; 450-10P = 0 therefore P = $45
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