Question

1. Consumer Surplus Question (10 points) The buyers side of the market for laser tag tickets consists of two types of consumers who demand curves are shown below. 18 12 Price ($/ticket) Price ($/ticket) 24 48 Tickets/yr Tickets/yr a. Graph the market demand curve on the graph below. Label everything (use units of 4 for the x-axis so it fits). Hint: It is helpful to determine the equations of the lines using y=mx+b for each so you can plug in prices and get quantities or plug in quantities and get price. b. Shade in the region that represents the total consumer surplus in the amusement park if tickets sell for $12 each. For 5 points of extra credit calculate the consumer surplus.

Answer 1

Answer

a. The equation of a linear inverse demand curve can be written as,

P = a - bQ , where 'a' is the intercept on the Y-axis, and 'b' is the slope of the demand curve. It is just like the linear equation, Y = mX+ b.

Let the following figure shows the demand curve of first type of consumers.

Price ($/ticket) 18 Tickets/yr 24

The Y-intercept of the above demand curve = 18

The slope of the above demand curve = (18 - 0) / (24 -0)

Or, slope of the above demand curve = 18 / 24 = 3 / 4

So, the equation of the above demand curve in its inverse form is as below;

P = 18 - (3/4)Q

We can write the above equation as,

(3/4)Q = 18 - P

Or, 3Q = (18 - P) * 4

Or, 3Q = 72 - 4P

Or, Q = (72 - 4P) / 3

Or, Q = 24 - (4/3)P

Thus, the equation of the demand curve of first type of consumers is,

Q = 24 - (4/3)P........(1)

Let the following figure shows the demand curve of second type of consumers.

Price (5/ticket) 12 Ticketsdyr 48

The Y-intercept of the above demand curve = 12

The slope of the above demand curve = (12 - 0) / (48 -0)

Or, slope of the above demand curve = 12 / 48 = 1 / 4

So, the equation of the above demand curve in its inverse form is as below;

P = 12 - (1/4)Q

We can write the above equation as,

(1/4)Q = 12 - P

Or, Q = (12 - P) * 4

Or, Q = 48 - 4P

Thus, the equation of the demand curve of second type of consumers is,

Q = 48 - 4P.......(2)

Let us now find the market price,quantity demanded by two types of consumers and, the market demand, that are shown in the following table;

Price(P)	Quantity demanded by first type of consumers[Q = 24 - (4/3)P]	Quantity demanded by first type of consumers[Q = 48 - 4P]	Market Demand
$0	24	48	72
$1	22.7	44	66.7
$2	21.3	40	61.3
$3	20	36	56
$4	18.7	32	50.7
$5	17.3	28	45.3
$6	16	24	40
$7	14,7	20	34.7
$8	13.3	16	29.3
$9	12	12	24
$10	10.7	8	18.7
$11	9.3	4	13.3
$12	8	0	8
$13	6.7		6.7
$14	5.3		5.3
$15	4		4
$16	2.7		2.7
$17	1.3		1.3
$18	0		0

The following figure shows the market demand curve;

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19 18 Q 0.18 Market Demand Curve 17 1.3, 17 16 2.7, 16 15 Q4. 15 14 5.3, 14 13 6.7, 13 12 08.12 PRICE 11 13.3. 11 10 18.7. 10 9 24.9 8 29.3,8 7 34.7,7 6 40,6 5 45.3,5 4 50.7.4 3 56,3 2 61.3.2 1 0.66.7. 1 72.0 0 0 4 8 12 16 20 24 28 32 36 48 52 56 60 64 68 72 76 40 44 QUANTITY

b. The shaded region of the triangle 'CS' shows the consumer surplus, when the price of the tickets is $12.

19 D 180, 18 Market Demand Curve 17 1.3, 17 16 2.7, 16 15 4. 15 14 CS 5.3, 14 13 6.7. 13 12 8. 12 PRICE 11 13.3.11 10 8 7.10 9 24,9 8 29.3.8 7 34.7,7 6 40,6 5 45.3,5 4 50.7, 4 3 56,3 2 0613,2 1 66.7, 1 72.0 0 0 4 8 12 16 20 24 28 32 36 48 52 56 60 64 68 72 76 40 44 QUANTITY

At $12, quantity demanded is 8 units. The maximum price, the consumer is willing to pay is $18.

$\therefore$ Consumer surplus = 1/2 * 8 * ($18 - $12)

Or, Consumer surplus = 4 * ($6)

Or,  Consumer surplus = $24

Thus, when the price of the tickets is $12 each, the consumer surplus is $24.

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