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nakungth nakungth
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7 years ago
The Catawba River City Park has a low demand D1 during work days, but on Saturday and Sunday demand increases to D2 on Saturday and Sunday.  The demand and marginal revenue functions are:
   D1 = P1 = 2 - 0.001Q1
   MR1 =  2 - 0.002Q1
   D2 = P2 = 20 - 0.01Q2
   MR2 = 20 - 0.01Q2
where Q = number of cars entering the park each day.  The marginal cost of operating the park is the same on weekdays and weekends:
   MC = 1 + 0.004Q.

a.   In order to control crowds, the park's management uses peak-load pricing.  This scheme controls crowds and makes sure the park is self-supporting.  Calculate the appropriate prices to charge, and determine the number of cars entering the park, Q1 and Q2.
b.   Explain how switching from a uniform pricing scheme to a peak load pricing scheme affects the market.
Textbook 
Microeconomics

Microeconomics


Edition: 8th
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#1
7 years ago
a.       
Equate MC to MR1, and the equate MC to MR2.  Compute P1 and Q1 and then P2 and Q2.
   1 + 0.004Q1 = 2 - 0.002 Q1
    0.006Q1 = 1
                     Q1  = 167 cars per day
   P1 = 2 - 0.001(167) = 2 - 0.167 = $1.83 per car       

Now compute P2 and Q2 by the method above.   
     1 + 0.004Q2 = 20 - 0.02Q2
         0.024Q2 = 1 9
                  Q2 = 792 cars per day
   P2 = 20 - 0.01(792) = 20 - 7.92 = $12.08 per car.

b.       
By switching from a uniform price to peak-load pricing, the firm can set MR equal to MC in each of the two periods.  By keeping MR equal to MC in each period the firm can increase "profit".  Since prices are closer to MC with peak-loading pricing, efficiency is increased.  The sum of consumer and producer surplus is increased.
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