Managerial Economics

In Class Exercise Six

1. Chez What has recently opened a coffee stand. They sell mostly breakfast items, particularly coffee and croissants.  The operators are particularly concerned about the demand for croissants.  In an effort to assess the wisdom of their pricing strategy, they asked an economist client to estimate the demand for croissants sold at Chez What.  He came up with the following information.

            Qd = 102 - 2P - 10P_c + 15P_a

                   Where P = the price of croissants,  P_c = the price of coffee sold at Chez What, and P_a = the price of coffee sold at the nearby Alpine bagel bakery

a. Suppose that the price of coffee at Chez What is $1 and that the price of coffee at the Alpine Bagel Bakery is $2 per cup.  Calculate the shortened version of the demand curve.

Demand:  Qd =         

For part b assume that the price of croissants is $1.

b. Calculate the point price elasticity of demand. Would Chez What increase profits by raising the price of croissants? Explain your answer.

   Elasticity = (slope)(P)/Q =

            Raise Price? - Explain why or why not?

2. Joe is evaluating the marketing strategy at his restaurant and inn. Suppose that in response to a $2.00 off" sales promotion for Spaghetti dinners, Joe finds that nightly dinner sales increase from 20 per night to 40.  Normally, the dinners sell for $6.00.

a.       What is the arc price elasticity of demand?

Arc Price Elasticity  =          _ (Q₁-Q₀)[(P₁+P₀)/2 ]         =         

                                                  (P₁-P₀)[(Q₁+Q₀)/2]                     

                        b. Would Joe increase revenues by further reducing the price?  What about profits?  Explain.      

                        Price reduction prompts revenue increase           Y / N / Can’t tell

                        Price reduction prompts profit increase               Y / N / Can’t tell

                        Explanation:

                        3.  Explain the relationship between Total Revenue (TR), Marginal Revenue (MR), the demand curve (as the price falls) and elasticity - both in words and

                         graphically.  Hint:  Start by saying, "if MR is positive ....."

                        4.  Bob increased the price of his bikes at Bob's Bikes from $200 to $250.  His sales declined form 10 bikes per week to 8 per week.  Calculate

                            the arc price elasticity (see equation in #2 above) and then calculate his total revenue before and after the price change.  Do your numbers make

                            sense?  Explain.

                       5.  Sarah owns a bakery.  When she decreased her cake price by 10%, her cake sales increased by 15%.  What is her implied price elasticity?

                        6.  Explain what "derived demand" means.  Explain the four factors that influence the derived demand elasticity of the following input (that produces chocolate pies):  chocolate.  Make any assumptions you need to make but they should be clearly stated.

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