Question
In: Economics
Consider a small town with two coffee shops, Star and Buck. If Star’s price is ??...
Consider a small town with two coffee shops, Star and Buck. If
Star’s price is ?? per cup of coffee and Buck’s price is ?? per cup
of coffee, then their respective monthly sales, ?? hundred cups of
coffee and ?? hundred cups of coffee, are given by the following
equations:
?? = 5 − ?? + ??
?? = 15 − ?? + ??
It costs $8 for both Star and Buck to produce a cup of coffee and
it costs $10 for Buck to produce a cup of coffee.
a. Are these two coffee shops producing substitute or
complementary products? How can you verify that based on the demand
equations?
b. For each of the coffee shop, write the profit as a function of
?? and ??.
c. Find each coffee shop’s best-response function.
d. Find the Nash Equilibrium price in this game.
e. Consider a twisted version of the above game: suppose that Star
has an option to advertise its coffee. This advertisement will cost
Star $5,000 if Star decides to use it, and it will change the
demand equations as:
?? = 12 − 0.5?? + 0.5??
?? = 10 − ?? + 0.5??
The marginal cost of each cup of coffee remains the same. Star has
to determine whether to use the advertisement and the price of its
coffee simultaneously. Find the Nash Equilibrium price in this
game. (Hint: this is still a simultaneous game. Star can choose to
advertise or not and its price, Buck can only choose its
price.)
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
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