Question

Katy runs a hair salon in the town of Dairy. She is debating whether she should extend her hours of operation. She figures that her sales revenue will depend on the number of hours the nail salon is open but staying open also increases her operational expenses. She calculates that every additional hour that she is open in the evening adds $120 to her costs. The table below shows the revenue from servicing clients during evening hour.

Hours Open	Total Revenue (dollars)
1	500
2	750
3	950
4	1,100
5	1,200
6	1,250

Using Marginal analysis, how many hours into the evening should Katy extend her nail salon's hours of operation.

Please show how you got the answer.

Answer 1

Answer

In order to maximize Profit a firm should produce that quantity at which MR = MC and if there is no such quantity then it should produce that quantity at which MR is greater and closest to MC i.e. MR is just above MC. where MR = Marginal Revenue and MC= marginal cost.

Let here Output number of hours of opening a salon.

Marginal cost is the additional cost incurred in order to produce 1 more unit of Output and here Marginal cost is the additional cost incurred in order to open salon for 1 more hour = 120(Given above).

Marginal revenue is the additional Revenue Generated by producing and selling 1 additional unit of Output.

Mathematically : MR(Q) = TR(Q) - TR(Q - 1)

where MR(Q) = Marginal Revenue from Q^th hour of opening a salon, TR(Q) = Total Revenue from Q hours of opening a salon.

We can see from above MR(4) = TR(4) - TR(3) = 1100 - 950 = 150

MR(5) = TR(5) - TR(4) = 1200 - 1100 = 100.

Thus, Here there is no Q sch that MR = MC and MR is just greater than MC when Q = 4 i.e. 4 hours of opening a salon.

Hence, Total number hours into the evening Katy should extend her nail salon's hours of operation are 4 hours.