BADM 606 Micro Final - Excel-Based Problems:  Fall 2001   Dr. Silver

 

Work all of the following problems using Excel to estimate the answers.  Credit will be given for form as well as substance, so make it look pretty!

 

In problems 1 through 3 below

  1. graph and label the following curves: demand, MC, MR, ATC, AVC,
  2. indicate using drawing tools (most likely arrows) the optimal quantity and price,
  3. then, estimate the values of P, ATC, and Q, and calculate the following: TR, TC, profit, and profit margin (profit/TC), and
  4. finally, determine the optimal strategy for the firm – i.e. whether to shut down or remain open.

 

1.                  A competitive producer in long-run competitive equilibrium having the following cost function

 

TC = 1,000,000 + 100Q + Q2

 

2.                  A monopolist having the following cost function: 

 

TC = 100,000 + 100Q + .1 Q2,

 

 and the following demand curve: 

 

Qd = 50,000 – 100P.

 

How does your answer change if the firm engages in marginal cost pricing, that is, sets P = MC?

 

3. ( From the West Ashley Gas Stations Problem )

The typical gas station in West Ashley with the following TC and inverse demand curves:

 

          TC = 600 + .8Q + .0001Q2   

          Q = 4000 - 2000 P , where

 

            P = price per gallon, in dollars, and

            Q = number of gallons purchased

 

            Using your graph, estimate the optimal price, quantity and profit for the typical service station.

 

 

4.   The airline market between Port Chester and Potsdam is duopolistic; only ABC and XYZ airlines dare to compete over this route.  Weekly demand for the “market” is given by

P = 700 - .05 Qm, where

P is the price of a ticket and 

Qm is weekly demand for flights over the route.

 

Assuming the two airlines match price, weekly demand for each airline is given by  P = 700 - .1Q, where Q is the number of tickets written by each airline per week.

 

The total cost of flying a passenger over the route, for either company, is given by TC = 100,000 + 100 Q + .05 Q2.

 

a.   Use Excel to graph the demand, marginal revenue, and marginal cost curves for an airline and find the optimal price to charge, if the two companies set the same price.  Find also the weekly profits for each airline.  Solve the equations to check your answer.

 

b.   Suppose ABC can “cheat” by lowering its price without retaliation by XYZ.  Show that ABC’s linear demand curve connecting its current equilibrium point and the market demand at P = 0, is given by P = 5831/3 – 1/24 QA, where QA is ABC’s weekly flights.  What is ABC’s optimal price and profits along this demand curve?

 

c.   Suppose we are initially at the point found in part a.  Now market demand increases to P = 800 - .05Qm and demand for each airline is P = 800 - .1Q if prices are matched.  Show that the number of flights per airline, at the original price, is 3000 per week. 

 

d.   Suppose also that any reduction in price from the original equilibrium price of $500 is matched by the other airline, that is, P = 800 - .1Q, but any increase in price is not matched.  The demand curve for an increase in price by either airline is given by P = 650 - .05Q.  Use Excel to graph the “kinked” demand curve, the MR, MC and ATC curves.  Will either airline either lower or raise its price given the assumptions stated above?  How does this compare with the price set and profits if the other airline matched the price increase?