Pizza Venice and Pizza Sun are two pizza restaurants in a town. The demand for pizzaat...

Pizza Venice and Pizza Sun are two pizza restaurants in a town. The demand for pizzaat Pizza Venice is given byQV= 14−PV+PS, while the demand for pizza at PizzaSun isQS= 8−2PS+PV. (Prices are in dollars and quantities are measured in 100customers). Pizza Venice has a unit cost of $4, while Pizza Sun has a unit cost of $2per pizza.

a.(4 points)Write the profit function for each restaurant in terms of PV and PS.

b.(8 points)Find each restaurant’s best reply function.

c.(6 points)Find the Nash Equilibrium price, quantity, and profit for each restaurant.

Expert Solution

The questions in this case are a typical example of nash equilibrium. Profit function can be derived by subtracting total costs from total revenues.

For best reply function, we need to fix each of the other firm's prices to be constant and find the function through first derivative.

Solving the 2 equations we got above, we'll get the nash equilibrium, quantities and the profits.

The working for all the sections is shown below.

Hope this helps. Do hit the thumbs up. Cheers!

Rahul Sunny answered 2 years ago

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