Price Competition in a Vertically Differentiated Market

[@rafaeladrumond1270]

Hello, Thank you for your explanation, it helped me a lot!!

[@MattBirch]

Glad to hear it!

[@nicholasgleason2993]

Thanks for the video. How do you quantify quality (v)

[@MattBirch]

That totally depends on the application. For a computer, it could be RAM or processor speed. For a car it could be horse power or fuel efficiency. It just depends.

[@ohad157]

Hey Matt, could you please direct me to a textbook that goes through a similar model like yours? I'm looking for the simplest of models but with firms choosing quality, unlike in your example. Thank you.

[@MattBirch]

Sorry for the late reply. This model is pulled from section 11.6 of Microeconomics, by Goolsbee, Levitt, and Syverson, 3e.

[@abdirashiidmohamedrashiida7553]

please are the same fancied and real product diffirentiation those one you have already explained ?

[@MattBirch]

If I understand you correctly, the main difference is that you would also choose the right location. That would be a 2-stage game. You would first solve for optimal prices as functions of locations (like I did in this video). Then you would write a profit function that is a function of locations only (since price is also a function of location), and maximize profit with respect to locations. I don't know if that makes sense or not.

[@Craic123]

can you do an assumption on product differentiation relaxes price competition

[@MattBirch]

I cannot do a video right now with the busy end of semester and the classes I have to do. But take your price that you solved for and take the derivative of it with respect to your differentiation. You will find a negative relation of more difference leading to higher prices.

[@MattBirch]

Does that make any sense or help at all?

[@Craic123]

@@MattBirch no please

[@MattBirch]

@@Craic123 I am sorry but I can't. At least not immediately. I will try to get to it later, but it will at least be a few days. What kind of question are you trying to answer?

[@MattBirch]

@@Craic123 : rewrite the equations for p1* and p2* with a D (for differentiation) in place of "v2-v1". Then take the derivative with respect to D and you get 1/3 for one of them and 2/3 for the other. As differentiation increases, so does price.

[@agyapongfrank8597]

Please solve this for me Suppose that the demand function of an industry can be described in the following way There are 1000 consumers uniformly distributed on the line segment [0, 1] Trans- portation costs are 10 per unit of distance . The industry consists of two firms with cost function C(q) = 10 + 20q Firm 1 is located at 0 and the other at 1 . ( a) Determine for each firm the individual demand function , the reaction function , the equilibrium price and profits when firms set prices simultaneously as in the Hotelling model . ( b) Assume that firm 1 has cost function C(q) = 10 + 20q while firm 2 has lower costs given by C(q) = 2 + 5q Compare the equilibrium prices and profits to part ( a) . ( ) Assume as in part (a) that both firms have cost function C(q) = 10 + 20q Suppose firm 1 sets its price first and firm 2 sets its price after observing firm choice . Compare the equilibrium prices and profits to part ( a).

[@MattBirch]

No. Sorry, but I don't do that.

[@balling220]

​@@MattBirchNot even a summary of the solutions, huh

[@MattBirch]

@@balling220 haha, I'm just a jerk like that. One guy even offered to pay me to do his homework for him. I refused.

[@balling220]

@@MattBirch Nevertheless, I want to know why (q2 = 1 - b)? Also, how do you derive u1 & u2 from the chegg question?

[@MattBirch]

For the question about q1 and q2 and b, it is because we assume everyone is buying one product of the other, so q1+q2=b. Not sure what you mean by the other question.

[@ashleyfratesi8050]

what if a=0, b>.5 t=2 c=0 for both firms.

[@MattBirch]

I am not sure what you are asking. My notation does not include an "a" or a "t".