ECON 321 Assignment 5

Let’s combine Assignment 4 and 5, so we’ll have a Cournot duopoly with firms that have both differentiated products and also different costs. We’ll give firm 1 the same demand parameters we’ve been using before, but we’ll give firm 2 the potential to have higher or lower demand response and also higher or lower costs.

First let’s quit the kernel to make sure we’re starting fresh (same as Evaluation >> Quit Kernel >> Local)

Quit[]

Now we need to set up an inverse demand system.

inversedemand1 =10-2(Subscript[q, 1])-(Subscript[q, 2])

inversedemand2=10-2(Subscript[b, 2])(Subscript[q, 2])-(Subscript[q, 1])

Firm 1’s Profit Maximization Problem (firm 1 has constant marginal cost 1)

profit1=(inversedemand1-1)(Subscript[q, 1])

FOC1 = D[profit1,(Subscript[q, 1])]==0

react1=Solve[FOC1,(Subscript[q, 1])]/.Rule-> Equal //Flatten // First

Firm 2’s Profit Maximization Problem (firm 2 has variable marginal cost (Subscript[c, 2]))

profit2=(inversedemand2-(Subscript[c, 2]))(Subscript[q, 2])

FOC2 = D[profit2,(Subscript[q, 2])]==0

react2=Solve[FOC2,(Subscript[q, 2])]/.Rule-> Equal //Flatten //First

Solve simultaneously to find the Cournot-Nash equilibrium:

qstars = Solve[{react1,react2},{(Subscript[q, 1]),(Subscript[q, 2])}] //Flatten

Evaluate the inverse demands and the profits to find what they are equal to at the equilibrium quantities:

pstars={inversedemand1,inversedemand2}/.qstars //Simplify

profitstars={profit1,profit2}/.qstars//Simplify