I\'m confused how to figure out optimal price when marginal cost is 0 like in th
ID: 1196232 • Letter: I
Question
I'm confused how to figure out optimal price when marginal cost is 0 like in the following problem:
A local tailor has two types of customers, private customers and department stores. The market of
private customers has a demand given by Qp = 2000–100P, and the market of department stores
has a demand given by Qs = 4000 100P. The marginal cost of one more alteration is constant
and equal to zero.
(a) Suppose that the tailor can charge different prices to each type of customer. What are the
optimal prices? What is the total profit?
(b) What is the value of each demand’s elasticity at the optimal price level?
(c) What is the total consumer surplus (for both groups)?
(d) Suppose that a regulation prohibits price discrimination. What is the optimal (uniform)
price? How much does the regulation cost the tailor in terms of forgone profits? What happens to
consumer surplus?
Explanation / Answer
Q=4000-100P.
The inverse demand function is therefore P = 40 –Q/100
MR = 40 – Q/50
Marginal cost here is given by MC = 0
Setting MR = MC for this segment yields
Q = 2,000 and at this quantity P = 40 –Q/100 implies that the price would have to be 20.
For the department store segment, demand is given by Q = 2000 – 100P.
The inverse demand function for this segment is P = 20 – Q/100 MR = 20 – Q/50.
Setting MR = MC for this segment yields Q = 1000 and P = 10.
Revenues from the individual customers are 2000*20 and from the department stores 1000*10.
Since MC = 0, the operating profits (or the total profits if there are no sunk or fixed costs) are simply equal to the total revenue of 50,000.
(b)
Since at the optimal point MR=MC=0, the demand elasticity has to be equal to –1 in both markets.
(c) To find the optimal price we have to find the total demand first.
The total demand is Q=100(40-P)+10(200-10P)=6000-200P.
The inverse demand is P=30-(Q/200).
From this you get TR=Q(30-(Q/200))=30Q-(Q2 /200), and MR=30-(Q/100).
To find the optimal price set MR = MC and get Q=3000 and P=15. The profit in this case is 45,000, and the cost to the tailor of the regulation is 50,000-45,000=5,000.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.