Name

A.  Taxi Rides

     You will find that some graph paper will help you organize your thinking as you go through this exercise. The graph is for your own use and will not be graded.

            The Calloway Cab Company has an exclusive franchise to provide taxi service between the airport and the downtown business district.  Its total cost function is TC = 1200 + 30Q + .50Q², where Q is the number of taxi rides per day.  The daily demand function for rides between the two destinations is Q = 180 - P, where P is the fare.

A1.   Write the equation for Calloway’s average total cost function and plot this

       relationship in your graph.    

                                               ATC = (1/Q) +  + Q

Calloway’s marginal cost function is MC = 30 + Q  (obtained by taking the derivative

      of the total cost function with respect to Q).   Plot this relationship in your graph.

Plot the market demand function in your graph.

A2.   Write the equation for Calloway’s marginal revenue as a function of Q.  (Recall

       that it has the same vertical intercept as the demand function but twice the slope.)

                                                 MR = + Q

   Plot the marginal revenue curve in your graph.

A3.   Using algebra, calculate Calloway’s profit maximizing output.  Q =

A4.   What price will it charge?       P =

A5.   What profit will it earn?     P =    

   Label this profit “P” in your graph.

B.  Lemonade I

            During the summer in Elmtown, lemonade is sold at small stands on street corners in residential neighborhoods.   All stands are independently owned and operated by school children.  They are also equally efficient and sell lemonade of the same quality.   Each stand has a U-shaped long run average cost curve that reaches a minimum value of  $.40 at q = 40 cups per day.  In addition, factor prices (for lemons, sugar, etc.) and production conditions are unaffected by the scale of the industry.   To a first approximation, therefore, lemonade in Elmtown is a constant cost competitive industry.    The daily Elmtown demand for lemonade is Q = 500 - 400P.

In a new graph plot the demand and long run supply curves for lemonade in Elmtown.

B1.  What are equilibrium price and quantity?                P₀ =

                                                                                     Q₀ =

B2.  How many stands are there and how many cups of lemonade is each selling per day?

                                                                                                N₀ =

                                                                                                q₀  =

B3.  What are the profit levels for the individual stand and for the industry as a whole?

                                                                                                p₀ =

                                                                                                P₀ =

B4.  How much consumer surplus are lemonade buyers as a group receiving?

                                                                                                C₀ =

B5.  How much social/economic surplus (i.e., “gains from trade”) is this market generating?

                                                                                                S₀ =

C.  Lemonade II

            Buffy Warren (age 11) lives in Elmtown and studied economics in fifth grade.  She sees that selling lemonade would be much more profitable if all stands were owned by a single firm and the entry of new ones prohibited.  Using money from an inheritance, she buys out all the existing stands and bribes the Elmtown City Council to give her an exclusive franchise.   She names her new company Lemonopoly.

C1.  Based on the delay demand for lemonade used in Part B., write the equation for Lemonopoly’s marginal revenue curve (i.e., MR as a function of firm output).

                                          MR = + Q

Plot this relationship in a second graph; again, for your own use.  Draw and label Lemonopoly’s marginal cost ( = average cost) curve in your graph.

C2.  What price will Lemonopoly charge and what quantity will it produce?

                        P₁ =                      Q₁ =

C3.  How many of the original stands will it close?   # closed =

C4.  What profit will it earn?            P₁ = 

Label this amount “P₁” in your second graph.

C5.  How much consumer surplus will lemonade buyers receive? C₁ =

Label this amount “C₁” in your graph.

C6.  How much social surplus will the market generate?    S₁ =

C7.  What deadweight loss will monopolization impose?          D = 

Label this amount “D” in your second graph.