- Submitted By: YMKim
- Date Submitted: 12/21/2013 10:35 PM
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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...