Answer:
with price discrimination
Domestic Price 7,000 Quantity 300
Profit (7,000 - 1,000) * 300 = 1,800,000
Foreing Price 9,000 Quantity 200
Profit (9,000 - 1,000) * 200 = 1,600,000
Total 1,600,000 + 1,800,000 = 3,400,000
no price discrimination:
Price 7,667 Quantity 500
Profit (7,667 - 1,000) x 500 = 3,333,500
Explanation:
Sales Revenue (Domestic)
[tex]R = P \times Q_d = (13,000 - 20Q_d) \times Q_d = -20Q_d^2 + 13,000Q_d\\R' = \frac{dR_{(q)}}{dq} = 13,000 - 40Q_d[/tex]
We now equalice against Marginal Cost:
13,000 - 40Qd = 1,000
Qd = 12,000/40 = 300
Price: 13,000 - 20(300) = 7,000
We do the same process with Foreing demand:
(17,000 - 40Qf) x Qf = -40Qf^2 + 17,000Qf
R' = -80Qf + 17,000
-80Qf + 17,000 = 1,000
Qf = 16,000/80 = 200
Pf = 17,000 - 40(200) = 9,000
If the company cannot do price discrimination then:
We solve for the inverse of both market:
PD=13,000 -20QD
QD = 650 - PD/20
we take the price restrictions:
PD < 13,000
PF= 17,000-40QF
QF = (17,000 - PF)/40 = 425
QF = 425 - PF/40
PF < 17,000
Now, we aggregate the demands:
(650 -P/20 ) + (425 -P/40) =
Q= 1,075 - 0.075P
Make the inverse
P = (1,075 - Q ) / 0.075 = 14.333,33 -13.33Q
And solve for the Quantiy and Price that maximize profit
R = (14.333,33 -13.33Q) x Q = -13.33Q^2 + 14,333.33Q
R' = R(q)/dq = -26.66Q + 14,333.33
-26.66Q + 14,333.33 = 1,000
Q = 500
P = 14,333.33 - 13.33(500) = 7,667
