Monopolist with vertical differentiation. Setup: demand that depends on both
quantity and quality (let's say P=2z(50-0.5Q)). Choose a cost of quality (let's say
F(z)=z^2). Let's say the marginal cost of production is c=0 (if you feel a bit
adventurous, pick up a non-zero marginal cost of production.
1. Show what happens to the demand curve when quality increases.
2. How much would the monopolist produce?
3. What is the quality the monopolist would choose? (For a question like this I
would give you the formula for a max/min of a quadratic function, so you do
not have to memorize it).
4. Show graphically the change in CS when z increases. In the same diagram
show the change in PS when z increases.
5. Based in your answer to Question 4, explain whether the quality produced by
the monopolist is the socially optimal quality (for the quantity produced by
the monopolist).
6. Calculate the total surplus and find the socially optimal quantity.
