Question

1. The managers at Air León are reviewing data on sandwich purchases on their flights to decide whether they should change the price at which they sell sandwiches to their passengers flying coach. On a typical flight the airline sells 72 sandwiches when they charge $3 per sandwich. When they set a price of $6, they sell 60 sandwiches per flight on average. If they set a price of $8, an average of 52 sandwiches are sold per flight. The airline managers were careful in reviewing data for comparable flights, and believe no factors other than the price explained the differences observed in quantities purchased.

a) What is the equation for this demand curve (Q as a function of p)?

b) Sandwiches are currently being sold on Air León flights for $11 and the marginal cost is $3. Check whether this satisfies the optimal mark-up rule. Is $11 the profit-maximizing price? If so, why? If not, should the price be raised or lowered, and why?

Answer 1

When price is $ 3 quantity sold is 72, when price is $ 6 quantity is 60 and when price is $ 8 quantity sold is 52.

We can see for every $ 1 increase in price the quantity demanded decreases by 4 units.

P = a - mQ

8 = a - m × 52

6 = a - m × 60

Subtracting second equation from first equation we get

2 = 8m

m = 0.25

a - mQ = P

a - 0.25 × 72 = 3

a = 3 + 18 = 21

Thus, the inverse demand function is

Demand function, Q = 84 - 4P

The optimal mark up rule is given by the following formula

First calculate the elasticity of the good at a price of $ 11

When P = $ 11

Q = 84 - 4 × 11 = 40 units

Differentiating Q wrt P, we get

(dQ/dP) = - 4

Elasticity of demand can be determined using the following equation

Mark up rule,

RHS = 1

Thus, the stated price that is $ 11 does not satisfy the optimal mark up rule. Here it is less thus the price must be increased.

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