Problem 2 – Static Economics A waterpark is the only one in a small town. Based
ID: 1211193 • Letter: P
Question
Problem 2 – Static Economics
A waterpark is the only one in a small town. Based on past summer season’s ticket sales, they estimate that the relationship between the monthly demand D (in persons) and price of a ticket p (in USD/person) in the town is described by p=44-0.0005D . The waterpark has a monthly fixed cost of 100,000 USD and variable cost of 16 USD per person.
a) What is the revenue-maximizing level of demand? What is the ticket price at this level? What is the profit?
b) What is the profit-maximizing level of demand? What is the ticket price at this level? What is the profit?
c) Compare and comment on the demand, prce, and profit levels you found in parts (a) and (b).
d) Draw and Excel plot of revenue, cost, and profit versus demand D and depict the locatons of the relevant values you found in parts (a), (b), and (d) above
Explanation / Answer
Ans-The relationship between the monthly demand D (in persons) and price of a ticket p (in USD/person) in the town is described by p=44-0.0005D .
TR=p*D=(44-0.0005D )D=(44D-.0005D2)
When revenue is maximised then dTR/dD=0
dTR/dD=44-.001D=0
.001D=44
D=44000, This is profit maximising level of demand.
Putting value of D we can find out value of p also.
p=44-(.0005*44000)
=44-22
=22, This is ticket price at that level.
TC=TFC+TVC
=100000+(16*44000)
=100000+704000
=804000
Profit=TR-TC
=(44000*22)-804000
=968000-804000
=164000, This is the profit.
b)When the condition profit maximisation exists it follows the condition MR=MC.
MR=dTR/dD=d(44D-.0005D2)/dD
=44-.001D
MC=d(100000+16D)/dD=16
At profit maximisation,
MR=MC
44-.001D=16
.001D=28
D=28000.-This is Profit maximising level of demand.
p=44-.0005D
=44-14
=30 This is profit maximising price.
TR=p*D=30*28000=840000.
TC=100000+(16*28000)=548000
profit=TR-TC=840000-548000=292000. This is profit.
c)In first case,p=22, D=44000, Profit=164000.
In second case, p=30, D=28000, profit= 292000.
price is less in 1st case than 2nd case.D is greater in 1st case than 2nd case and profit is less in 1st case than 2nd case.
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