Desi Pizza, Ltd, provides delivery and carryout service to the city of Surrey an
ID: 1216464 • Letter: D
Question
Desi Pizza, Ltd, provides delivery and carryout service to the city of Surrey and surrounding areas. An analysis of the daily demand for its super-supremo-wombo-combo paneer-dripping pizzas reveals the following demand equation:
Qx = 2,000 - 100Px – 2.5PS + 0.01CSP + 500S
where Qx is the quantity measured by the number of pizzas per day, Px is the price ($), PS is a price index for soda pop, CSP is the college student population and S, a binary or dummy variable, equals 1 on Friday, Saturday and Sunday and zero otherwise.
Currently Px = $10, PS = 100, and CSP = 25,000
(a) Calculate the quantity demanded of pizzas on Tuesdays and Fridays.
(b) Calculate the price elasticity of demand for Desi pizzas on theses two days.
(c) If Desi Pizza, Ltd is primarily interested in maximizing revenue, should they charge the same price everyday of the week? If not, what prices should they charge?
(d) If the cost per pizza is $5.00 and Desi Pizza, Ltd., behaves as a profit-maximizing monopolist, should they charge the same price everyday of the week? If not, what prices should they charge?
Explanation / Answer
Qx = 2,000 - 100Px – 2.5PS + 0.01CSP + 500S = 2,000 - (100 x 10) - (2.5 x 100) + (0.01 x 25,000) + 500S
= 2,000 - 1,000 - 250 + 250 + 500S
Qx = 1,000 + 500S
(a)
(i) On Tuesday, S = 0
Qx = 1,000
(ii) On Friday, S = 1
Qx = 1,000 + (500 x 1) = 1,000 + 500 = 1,500
(b)
(i) On Tuesday, Price elasticity = (dQx / dPx) x (Px / Qx) = - 100 x (10 / 1,000) = - 1
(ii) On Friday, Price elasticity = (dQx / dPx) x (Px / Qx) = - 100 x (10 / 1,500) = - 0.67
(c) Qx = 2,000 - 100Px – 2.5PS + 0.01CSP + 500S
Qx = 2,000 - 100Px - (2.5 x 100) + (0.01 x 25,000) + 500S
= 2,000 - 100Px - 250 + 250 + 500S
Qx = 2,000 - 100Px + 500S
Since demand function is different on different days, uniform price should not be charged.
(i) On Friday, Saturday & Sunday: S = 1
Qx = 2,000 - 100Px + 500 = 2,500 - 100Px
100Px = 2,500 - Qx
Px = 25 - 0.01Qx
Total revenue, TR = Px. Qx = 25Qx - 0.01Qx2
TR is maximized when dTR / dQx = 0
25 - 0.02Qx = 0
0.02Qx = 25
Qx = 1,250
Px = 25 - (0.01 x 1,250) = 25 - 12.5 = 12.5
(ii) On Monday, Tuesday, Wednesday & Thursday: S = 0
Qx = 2,000 - 100Px + 0 = 2,000 - 100Px
100Px = 2,000 - Qx
Px = 20 - 0.01Qx
Total revenue, TR = Px. Qx = 20Qx - 0.01Qx2
TR is maximized when dTR / dQx = 0
20 - 0.02Qx = 0
0.02Qx = 20
Qx = 1,000
Px = 20 - (0.01 x 1,000) = 20 - 10 = 10
(d) Monopolist maximizes profit by equating MR with MC (= 5) where MR = dTR / dQx
(i) On Friday, Saturday & Sunday,
dTR / dQx = 25 - 0.02Qx
Equating with MC,
25 - 0.02Qx = 5
0.02Qx = 20
Qx = 1,000
Px = 25 - (0.01 x 1,000) = 25 - 10 = 15
(ii) On Monday, Tuesday, Wednesday & Thursday:
dTR / dQx = 20 - 0.02Qx
Equating with MC,
20 - 0.02Qx = 5
0.02Qx = 15
Qx = 750
Px = 20 - (0.01 x 750) = 20 - 7.5 = 12.5