We are operating a winter lodge. Our market consists of two segments: locals and

Question

We are operating a winter lodge. Our market consists of two segments: locals and visitors. To service each customer, there is a MC of $10.00. Marginal cost is equal to average cost. The demand curve for visitors is Q = 500 - 10P, and for locals, it is Q = 500 - 20P. 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. 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 as in Question 1. You are the CEO of a pharmaceutical institute that owns the rights to No More Baldness. You ask your chief economist to analyze the pricing and investment decisions facing the product. The economist estimates that No More Baldness has the following demand curve: P = 101 -.0002Q The marginal cost for a No More Baldness tablet is $1. Average cost is equal to marginal cost. What is the profit-maximizing price and quantity? What is your profit? Suppose that you capacity is 1,000,000 tablets per year. What is your optimal price and quantity given the production constraint for one year? What are your profits?

Explanation / Answer

1(a)

For Visitors:

Q = 500 - 10P

The inverse demand function: P = 50 - 0.1Q

TR = P*Q = 50Q - 0.1Q2

MR = 50 - 0.2Q

For equilibrium, condition is : MR = MC

=> 50 - 0.2Q = 10

=> 0.2Q = 40

=> Q = 40 / 0.2 = 200

P = 50 - 0.1(200) = $30

For Locals:

Q = 500 - 20P

The inverse demand function: P = 25 - 0.05Q

TR = P*Q = 25Q - 0.05Q2

MR = 25 - 0.1Q

For equilibrium, condition is : MR = MC

=> 25 - 0.1Q = 10

=> 0.1Q = 15

=> Q = 15 / 0.1 = 150

P = 25 - 0.05(150) = $17.5

2.

Q =1000 - 30P

The inverse demand function: P = 33.33 - 0.033Q

TR = P*Q = 33.33Q - 0.033Q2

MR = 33.33 - 0.066Q

For equilibrium, condition is : MR = MC

=> 33.33 - 0.066Q = 10

=> 0.066Q = 23.33

=> Q = 23.33 / 0.066 = 353.48

P = 33.33 - 0.033(353.48) = $21.67

TR = P*Q = $21.67*353.48 = $7659.91

TC = MC*Q = $10*353.48 = $3534.8

Profit = TR -TC = $7659.91 - $3534.8 = $4125.11

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