Managerial Economics
The Players Theater Company
Course : S3 Asia MBA
Name : Myoung-Jin An (MJ)
Student No. : 13210690776
0. Demand function
Q = 117-6.6P+1.66Ps-3.3Pr+0.00661I
0. Given data
P = $30, Ps = $50, Pr = $40, I = $50000 → Q = 200.5 ≒ 200
0. Summary of lecture : Own price elasticity
Simplify demand function by substituting numbers except P
Q = 398.5-6.6P → 6.6P = 398.5-Q → P = 60-0.15Q (round-off)
Calculate own price elasticity
η = (ΔQ/Q)/(ΔP/P) = (ΔQ/ΔP)*(P/Q) = (-6.6)*(30/200) = -0.99 ≒ -1 (i.e. unit elastic)
1. Cross-price elasticity for symphony and for meals
a. Simplify demand function by substituting numbers except Ps
Q = 117.5+1.66Ps
Calculate cross-price elasticity for symphony
η = (ΔQ/Q)/(ΔPs/Ps) = (ΔQ/ΔPs)*(Ps/Q) = (1.66)*(50/200) = 0.415 (i.e. positive → substitutes)
b. Simplify demand function by substituting numbers except Pr
Q = 332.5-3.3Pr
Calculate cross-price elasticity for meals
η = (ΔQ/Q)/(ΔPr/Pr) = (ΔQ/ΔPr)*(Pr/Q) = (-3.3)*(40/200) = -0.66 (i.e. negative → complements)
2. Income elasticity
Simplify demand function by substituting numbers except I
Q = -130+0.00661I
Calculate income elasticity
η = (ΔQ/Q)/(ΔI/I) = (ΔQ/ΔI)*(I/Q) = (0.00661)*(50000/200) = 1.6525
If Pr = $50,
3. What happen?
Change demand function by substituting new numbers except P
Q = 365.5-6.6P → 6.6P = 365.5-Q → P = 55-0.15Q (round-off)
It means that increasing Pr (i.e. complements price) leads to decrease own demand as below(4,5)
4. Q = ?
Calculate Q
Q = 117-6.6P+1.66Ps-3.3Pr+0.00661I
P = $30, Ps = $50, Pr = $50, I = $50000 → Q = 167.5 ≒ 167
60
55
0
P
Q
365.5
398.5
P = 55-0.15Q
P = 60-0.15Q
←
60
55
0
P
Q
365.5
398.5
P = 55-0.15Q
P = 60-0.15Q
←
5. Demand curve
6. Own price elasticity
Calculate own price elasticity again
η = (ΔQ/Q)/(ΔP/P) = (ΔQ/ΔP)*(P/Q) = (-6.6)*(30/167) = -1.19 (round-off) (i.e. <-1 → elastic)
7. Maximized? Or to maximize total revenue, P = ?
a. Own price elasticity is not -1 (i.e. unit elastic), so total revenue...