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

a) Equation of Demand Curve :

Q=a+bp

Q=Quantity Demanded

p=Price

b=(Change in Quantity)/(Change in Price)

a=Quantity intercept ie Quantity demanded at Price =0

p1=$3, Q1=72

p2=$8, Q2=52

b=(Change in Quantity)/(Change in Price)=(Q2-Q1)/(p2-p1)=(52-72)/(8-3)=-20/5=-4

Q=a-4p

p3=6, Q3=60

60=a-4*6

a=60+24=84

EQUATION FOR THE DEMAND CURVE:

Q=84-4p

b)

Profit Maximizing Price ,

No, $11 is not Profit maximizing Price . $11 gives a profit of $320

Price of $12 will maximize Profit at $324, as shown below:Price needs to be raised.

	Marginal Cost			$3
	p	Q	A=(p-3)	B=Q*A
	Price	Demand	Unit	Total
		(84-4*p)	Contribution	Contribution
	$3	72	0	$0
	$4	68	1	$68
	$5	64	2	$128
	$6	60	3	$180
	$7	56	4	$224
	$8	52	5	$260
	$9	48	6	$288
	$10	44	7	$308
	$11	40	8	$320
	$12	36	9	$324
	$13	32	10	$320
	$14	28	11	$308
	$15	24	12	$288
	$16	20	13	$260
	$17	16	14	$224
	$18	12	15	$180
	$19	8	16	$128
	$20	4	17	$68