Question

In the year 2005, in Anytown, suppose that one person is willing to pay $1,000 for relief from hay fever; another two are willing to pay $350; about five more are willing to pay $50; one is willing to pay $40; one is willing to pay $35; one each is willing to pay $34, $32, $30, and $28; about a dozen are willing to pay $10; four are willing to pay $5; and half of the rest of the town (another 75 people) are willing to pay $1. a. Draw the demand curve for hay fever relief in Anytown. b. What is the potential total benefit (total of incremental value) from relief of hay fever if it is provided to everyone who asks? To everyone willing to pay $35 or more? c. If the price of hay fever medication is $20, what is the quantity demanded? What is the consumer surplus (total net value or benefit) for those who are willing and able to pay for the hey fever medication?

Answer 1

Demand schedule can be derived as follows.

Price	Quantity
$1000	1
$350	2+1=3
$50	5+3=8
$40	1+8=9
$35	1+9=10
$34	1+10=11
$32	1+11=12
$30	1+12=13
$28	1+13=14
$10	12+14=26
$5	4+26=30
$1	75+30=105

The schedule is derived commulatively, as who are willing to pay $1000, would be also willing to pay $350 and $50, etc, and are hence included.

(a) The demand curve is plotted as below.

(b) The total benefit is basically the consumer surplus or area below the demand curve, for price equal to lowest possible ($1 in this case). It is the sum of areas for which consumers are willing to pay for an additional unit. We can put the table we derived above in use, to find that. We add columns to find the area of additional units people are willing to buy at the price.

Price	Quantity	Areas as
$1000	1	$1000*1=$1000
$350	2+1=3	$350*2=$700
$50	5+3=8	$50*5=$250
$40	1+8=9	$40*1=$40
$35	1+9=10	$35*1=$35
$34	1+10=11	$34*1=$34
$32	1+11=12	$32*1=$32
$30	1+12=13	$30*1=$30
$28	1+13=14	$28*1=$28
$10	12+14=26	$10*12=$120
$5	4+26=30	$5*4=$20
$1	75+30=105	$1*75=$75

Potential total benefit is the sum of the last column, ie $2364, which is the Conusmer Surplus for if price is less than or equal to $1.

The potential total benefit to everyone who is willing to pay $35 or more is the sum of area between and including $1000 and $35 price, ie $2025.

(c) If the price is $20, then product demand would be met by everyone who are willing to pay more than or equal to $20. As can be seen, at $28, the quantity demanded is 14, and below $28, there are one who are willing to pay $10, and hence will not buy the product. Hence, at $20, quantity demanded is equal to 14.

The consumer surplus (CS) will be the sum of area for prices more than $20, ie $2149.

Note: In case the simple formula is applied, the CS will be a bit different. According to the formula, CS is , and in that case, , and hence, CS would be $2084, not $2149. But in this case, applying the direct formula seems oversimplified.