Question

Fun City has decided to build a new municipal water park with pools, water slides, and so forth. You have been hired to conduct a study to determine if the water park can pass the test. A nearby and very similar city currently has a water park similar to the one Fun City is considering. The nearby city currently charges $10 for admission and, on a typical day, attracts 4,000 persons. Last year, it charged $15, but only attracted 3,000 paying customers.

1. Assuming that the demand curve for water parks is linear, estimate the net benefits received by those using the Fun City water park, if Fun City charges an admission price of $12.50. [NOTE: You need not compute the actual amount; just use a graph and clearly indicate the area that represents the net benefit amount.]

2. By how much, and in what direction, would the net benefits received by those using the water park change if Fun City charges a $15.00 admission price, rather than $12.50? [NOTE: This time compute the actual dollar value.]

Answer 1

In both the questions, we need to show the consumer surplus gained as a result of the price variation.

a)

As the demand curve is linear, from standard line equation using 2 points we get the demand curve equation to be

P= 60 - 2D

The triangular area indicated by (1) is the net benefits of the consumer when fun city charges $12.50. Take a look at the graph.

On computing the area, the benefits = ½(30-12.5)(35×100)

= $30,625 .....(A)

b)

As the price charged increases, the net benefits decreases or moves leftwards.

Take a look at the graph below. Area with the zig zag pattern represents the fall in benefits.

The current benefits = ½(30-15)(30×100)= $22,500...(B)

So, the loss in benefits equals to (A)-(B)

= $30,625 - $22,500

= $ 8,125

Therefore benefits decrease by $8,125

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