Question

It is a hot day at the beach. Ice water costs $1 per bottle and this is your only option. Your marginal benefit for water follows the equation MB = $10 - $x.

x is represents the number of bottles of ice water you have had. So, for example, the marginal benefit of the first bottle is $10 - $1 = $9. The MB of the 2nd bottle is $8 .. and so on.

Assuming you are an economically rational consumer how much consumer surplus will you achieve when you are done for the day?

a.36 or 40.5 ... depending on whether you found the area of the triangle or added up each purchase incrementally.

   

b.9

   

c.26 or 27.5 ... depending on whether you found the area of the triangle or added up each purchase incrementally.

   

d.81

Please give me the answer and explain it thanks！

Answer 1

Let's first find out how many bottles will you buy. Each bottle costs, $1 so you will buy until the MB is $1, which you can see will be from the 9th bottle, as MB = $10-$x, where with x=9, MB=$10-$9 = $1, which is equal to the cost of each bottle.

Your consumer's surplus from the first bottle is equal to the MB you get minus its cost for you, i.e. ($10-$1) -$1 = $8

Your consumer's surplus from the second bottle is equal to the MB you get minus its cost for you, i.e. ($10-$2) -$1 = $7

and so on

and finally

Your consumer's surplus from the ninth bottle is equal to the MB you get minus its cost for you, i.e. ($10-$9) -$1 =$0

Hence the total surplus you get is:

$8+$7+$6+$5+$4+$3+$2+$1+$0= $$36 (this is what you get when you add each purchase incrementally).

You can also find the area of the triangle, where P=$9 (vertical intercept), and Q=9 (horizontal intercept). The area will be $9*9/2 = $40.5

Hence the right answer is a.