we are opening a winter lodge. our market consist of two segments: locals and vi

Question

we are opening a winter lodge. our market consist of two segments: locals and visitors. to service each customer, there is a MC of $10. marginal cost is equal to average cost. the demand curve for visitors is Q=500- 10 P, and for locals, it is Q=500-20P.

A. Determine the equilibrium P and Q for each market segment and the total profit in each segment.

the overall market (both segments) in question 1 is Q= 1000-30P.

B) what is the equilibrium P and Q, and the total profit by charging a uniform price?

The marginal cost and average cost assumptions are the same.

Explanation / Answer

MC of $10. marginal cost is equal to average cost.

the demand curve for visitors is Q=500- 10 P

P = (500 - Q) /10 => 50 - Q/10

TR = Px Q = 50 Q - Q2/10

MR = d TR / d Q => 50 - Q/5

At equilibrium, MR = MC

50 - Q/5 = 10

Q = 40 x 5 => 200

P = 50 - 200/10 => 30

TR = P x Q => 30 x 200 = 6000

AC = 10 and TC = AC x Q => 200x10 = 2000

Profit = TR - TC => 6000 - 2000 = 4000

for locals, it is Q=500-20P.

P = (500 - Q) / 20 => 25 - Q/ 20

TR = Px Q =25 Q - Q2/ 20

MR = d TR / d Q => 25 - Q/ 10

At equilibrium, MR = MC

25 - Q/ 10 = 10 => Q = 15 X 10

Q = 150

P = 25 - 150 / 20

P = 17.5

TR = 17.5 X 150 => 2625

TC = 10 X 150 = 1500

Profit = 2625 - 1500 =>1125

B) Q= 1000-30P

P = (1000 -Q ) / 30 => 33.33 - Q / 30

TR =  33.33Q - Q2 / 30

MR =  33.33 - Q / 15

AT EQUILIBRIUM, MR = MC

33.33 - Q / 15 = 10

TOTAL Q = 15 X 23.33 => 350

UNIFORM P = 33.33 - 350 / 30

P = 21.67

TR = 21.67 X 350 =>7584.5

TC = 10 X 350 = 3500

PROFIT = 7584.5 - 3500 =>4084.5

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