Wonderland is an amusement park in City A. The manager would like to estimate th

Question

Wonderland is an amusement park in City A. The manager would like to estimate the linear demand curve of the park tickets using the data of 2013 and 2014. In 2013, the price for per ticket is 10$ and 30,000 tickets were sold. In 2014, the price for per ticket increased to 15$, and 25,000 tickets were sold.

a) Please estimate the demand curve of the tickets for Wonderland, and draw the graph of the curve.

b) In order to sell at least 28,000 tickets in 2015, what is the highest price the manager would set for one ticket? (demand curve is unchanged)

c) What is the demand elasticity of Wonderland tickets at the 2013, 2014, 2015 equilibrium price and quantities?

d) Suppose experts estimates a coming recession on city A’s economy in 2016, the attraction of Wonderland will also be negatively affected. Thus manager anticipate a new demand curve. In which direction do you think the new demand curve will move from the previous one? In order to keep the park popular, what price strategy you will suggest the manager?

(Please show full work how you solved question)

Explanation / Answer

(a) The linear demand function be: Q = a - bP where Q: Quantity, P: Price

So:

30,000 = a - 10b ..... (1)

25,000 = a - 15b .... (2)

(1) - (2) gives:

5,000 = 5b

b = 1,000

Substituting in (1):

30,000 = a - (10 x 1,000)

a = 40,000

So, demand function is:

Q = 40,000 - 1,000P

(b)

Q = 28,000

So: 28,000 = 40,000 - 1,000P

1,000P = 12,000

P = $12

(c)

Price elasticity of demand, eP = Change in quantity demanded / Change in price

2014: eP = [(25,000 - 30,000) / 30,000] / [(15 - 10) / 10] = - 0.17 / 0.5 = - 0.34

2015: eP = [(28,000 - 25,000) / 25,000] / [(12 - 15) / 15]

= 0.12 / - 0.2 = - 0.6

(d)

A recession will reduce consumer income, which will shift the demand curve upward towards left, thus decreasing demand.

So, a price reduction will be suitable.

However, demand is inelastic, since absolute value of elasticity is less than 1. So a price decrease may result in a fall in total revenue, since demand will not increase to a large extent, corresponding to a price cut. Therefore, it is advisable to keep the price unchanged.

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