# Class 06

Class 06 of 23 September 2015

Duopoly: Two Firms in Quantity Competition

See discussion of the Cournot Duopoly Model in Martin text, pp 62-77.

• Saudi Arabia: application of basic elasticity mindset

» see blog post: if small in market, cutting output doesn’t raise prices enough to raise revenue. so do the Saudis care about revenue? and so on

» always question claims that someone is trying to do this or that to sway a market!!

• Miller versus Budweiser

› what happens if (rather, when) Budweiser decides to enter Miller Lite’s monopoly market with Bud Lite? or more precisely, in terms of our models what is the rational strategic response of Miller to Anheuser-Busch?

› reaction curve

» rational response to a shrinking market is to cut output

» end game (with similar cost structures and similar sized CEO egos) is a symmetric market.

= can begin by shifting Miller Lite’s demand curve in → MR moves in → optimal Q ↓

= draw reaction curve for each: intersection is equilibrium, can pick an arbitrary initial point and see that you move towards it

= requires graph intuition but (i) output is more than monopoly level [a diagonal where q1 + q2 = monopoly level lies underneath] and (ii) less than p=MC level [similar diagonal]

› algebraic analysis

› straightforward, allows solving for case of n symmetric firms

› bottom line is that total Q = n x q* for q* optimum for a single firm. this quantity approaches that of our competitive p = MC firm

› in other words, more firms = more competition ⇒ lower price and lower DWL.

• we need this and similar algebraic results for precision when we talk about mergers, how the number of firms should change with the size of the market and other questions of likely interest