Assume that there are two hair salons located on Main Street which is 1 mile in...

Assume that there are two hair salons located on Main Street which is 1 mile in length. Salon A which is located at the east end of the Main Street has a constant unit cost of $5and Salon B which is located at the west end of the Main Street has a constant unit cost of $10. There are 1000 potential customers who live along the street and they are uniformly spread out along the street. Customers are willing to pay $40 for a hair-cut that is done at their home. If a customer has to travel to get a hair-cut, then a there and back travel cost of $5 per mile is incurred. Suppose that each salon wants to set a price for a hair-cut that maximizes salon’s profit.

a- Salon A and Salon B choose their prices simultaneously. What are the equilibrium prices? What are the equilibrium profits? Do these two salons serve all customers?

b- Suppose Salon A’s unit cost is $a and Salon B’s unit cost is $10. For which values of a all customers are not served.

Expert Solution

a. If both salons choose prices simaltaneously, both firms will choose a price of 35$ such that they could serve their half of the street. (Customer is willing to pay 40$ at home and 5$ per mile for travelling, thus a customer upto half a mile away would be willing to pay 35$+2.5$+2.5$ for travelling) (They could each charge 30$ so that all consumers can afford it but even then only 500 customers will come to their salon as they will visit the one closer and therefore their profit will be less)

Thus the equilibrium prices are 35$ for both salons

Equilibrium profits=500*35$-500*5$=15,000$ for salon A

=500*35$-500*10$=12,500$ for salon B

Yes, these salons serve all customers(500 each)

b. if salon A's unit cost is $a, the value of a such that not all customers are served is a>35

If the unit cost of salon A is greater than 35, the customer half a mile away would have to pay 35+2.5+2.5=40$ for cutting at salon A, however if a is greater than 35,the customer will not be willing to pay more than 40$ and thus will not be served.

Hope it helps. Do ask for any clarifications required,

Rahul Sunny answered 1 year ago

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