In: Economics
The demand curve of the only customer in the amusement park is QD = 200-P. The park charges an admission fee of 100, while each ride costs 9.
1. Determine the supply curve of the park.
2. Determine the producer surplus without distortions in the
market.
3. Determine the consumer surplus without distortions in the
market.
4. Price at which dead weight loss is minimized?
5. At which quantity does it occur (in rides)?
6. if the government wishes to limit the number of rides per person
to at most 5 per person, calculate the loss in economic
efficiency.
Answer: (1) The entry fee for the park is = 100 and each ride cost 9.
So, the cost of supply of 1 ride = 100 + 9 = 109
Cost of supply of 2 rides = 100 + 2*9 = 118
Cost of supply of 3 rides = 100 + 3*9 = 127
So, supply curve is : P = 100 + 9Qs
Or, 9Qs = P - 100
Or, Qs = (P/9) - 100/9 .....This is the supply curve of the park
(2). To determine the producer surplus first we need to find out Equilibrium price and quantity of number of rides and price.
QD = 200 - P = QS = (P/9) - 100/9
Or, 200 - P = P/9 - 100/9
Or, 1,800 - 9P = P - 100
Or, 10P = 1,900
Or, P = 1,900/10 = 190.
So, Equilibrium price = $190
Equilibrium number of rides : Q = 200 - P = 200 - 190 = 10.
Producer surplus without distortion in the market will be producer surplus at P = 190 and Q = 10
Inverse supply curve is : P = 100 + 9Qs
It means at Qs = 0, P = 100 , It shows the intercept of supply curve at vertical axis.
Producer surplus = (1/2)*base*height
Producer surplus = 0.5*10*($190 - $100) , base is Q = 10 , height is P difference between intercept and equilibrium price
Producer surplus with out distortion = 0.5*10*$90 = $450.
(3) Consumer surplus without distortion will be consumer surplus at P = 190 and Q = 10 .
Demand curve: QD = 200 - P
Or, P = 200 - Q
It means at Q = 0 , P = 200, this 200 at price axis is the vertical axis intercept.
C.S = (1/2)*base*height
C.S = 0.5*10*($200 - $190) , base is the equilibrium Q = 100, height is the difference in price between vertical intercept and equilibrium price i.e $200 - $190 = $10
C.S = 0.5*10*$10 = $50.
So, Consumer surplus without distortion is = $50.
(4). Price at which dead weight loss (DWL) will be minimum is $190 , where $100 is entry fee. It means $90/ride is that where dead weight loss is minimised. The efficient price is $190, which shows lowest minimum dead weight loss (DWL).
(5). The DWL is minimised at Q = 10 , This Q = 10 is efficient quantity where there is no distortion. At Q = 10 and P = 190 , DWL is minimised.
(6). If Government wishes to limit the rides 5 per person. Then Q = 5.
In the demand equation if Q = 5, then P = 195.
In supply equation if Q = 5 , then P = 100 + 9*5 = 145.
Therefore , C.S at P = 195 , Q = 5 will be
C.S = (1/2)*base*height
C.S = 0.5*5*($200 - $195)
C.S = 0.5*5*$5 = $12.5
Now, P.S at P = $145 , Q = 5 is
P.S = (1/2)*base*height
P.S = 0.5*5*$(145 - 100)
P.S = 0.5*5*$45 = $112.5
Therefore, C.S + P.S under distortion is = $12.5 + $112.5
(C.S + P.S) under distortion = $125.
When there was no distortion then C.S + P.S = $50 + $450
(C.S + P.S ) without distortion = $500.
Therefore loss in economic efficiency due to Government limit the number of ride per person is $500 - $125 = $375. (Ans).