Assume annual market demand for UVic coffee mugs is given by P=20-Q, where P is the price, and Q is the quantity of these fancy collector's items. In this market, consider the firm Dominant with cost function C1(Q1) Q1+25, where Q1 is the Dominant's quantity. Let Dominant initially be a monopolist
(a) Derive the monopoly price and quantity of Dominant both graphically and mathematically. In your graph show what are Dominant's monopoly profits.
Now assume that a potential competitor Difficult-To-Dominate (DTD) with cost function C2(Q2)- 3Q2+16 considers entering the market. If DTD indeed enters, then both firm next arrive at a subgame in which they compete a la Cournot (that is, in the subgame both firms choose their quantities simultaneously, while each firm holds Cournot conjectures regarding its rival's behaviour). If DTD does not enter then Dominant charges the monopoly price. DTD gets a payoff of zero then.
(b) Present the game tree of the game between Dominant and DTD. [Hint: If you cannot answer this question fully, at least sketch the Cournot subgame carefully.]
(c) Assume in this part of the question that DTD has indeed entered, so that the Cournot subgame referred to in Gb) applies. Derive the so-called best response functions of Dominant and DTD. Derive the Nash equilibrium to the Cournot subgame Add a stage to the game and assume that Dominant makes a pre-announcement regarding her production amount before the entry decision of DTD
(d) Derive the limit quantity, that is, derive the minimum quantity that Dominant has to pre-announce in order to successfully impede entry of DTD. In this question assume that Dominant's announcement sounds fully credible to DTD.