Lecture 5 Oligopoly 2010

Lecture 5 Oligopoly 2010 - ECON 4109H LECTURE 5 Oligopoly...

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Unformatted text preview: ECON 4109H LECTURE 5 Oligopoly October 25, 2010 ECON 4109H LECTURE 5 Oligopoly How does competition among firms depend on characteristics of demand for firms’ output, the nature of firms’ cost functions, and the number of firms? Will benefits of technological improvements be passed on to consumers? Will reduction in the number of firms generate less desirable outcomes? To answer these questions we will build a model of oligopoly (competition among a small number of sellers). ECON 4109H LECTURE 5 General Model Single good produced by n firms. Cost to firm i of producing q i units of a good C i ( q i ) ; C i is an increasing function (more output more costly to produce). All output sold at single price, determined by demand for the good and firms’ total output. With output Q , market price is P ( Q ) . P is that inverse demand function. Assume that P is a decreasing function when positive: if total output increases, then price decreases (unless already zero). Output of firm i is q i ⇒ price is P ( ∑ i q i ) . profit=revenue minus cost: π ( q 1 , . . . , q n ) = q i P ( X i q i ) - C i ( q i ) ECON 4109H LECTURE 5 Cournot Oligopoly Game Players The firms Actions Each firms’ set of actions is the set of possible outputs Preferences Firms preferences represented by profits. ECON 4109H LECTURE 5 Duopoly with Constant Unit Cost and Linear Inverse Demand 2 firms. C i ( q i ) = cq i Inverse Demand: P ( Q ) = α- Q , if Q 6 α ; 0, if Q > α . Assume that c < α so that for some value of total output Q , the market price > unit cost. ECON 4109H LECTURE 5 Duopoly with Constant Unit Cost and Linear Inverse Demand π 1 ( q 1 , q 2 ) = q 1 ( P ( q 1 + q 2 ) - c ) = q 1 ( α- c- q 1- q 2 ) , if q 1 + q 2 6 α ;- cq 1 , otherwise. ECON 4109H LECTURE 5 Duopoly with Constant Unit Cost and Linear Inverse Demand Observe that a higher quantity for firm 2 leads to a lower price, and hence a lower profit for firm 1 when producing any quantity q . Observe that ∂π 1 ∂ q 2 ∂ q 1 ( q 1 , q 2 ) = - 1 < 0 if q 1 + q 2 < α , and is equal to 0 otherwise....
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This note was uploaded on 01/19/2012 for the course ECON 4109H taught by Professor Notsure during the Fall '09 term at Minnesota.

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Lecture 5 Oligopoly 2010 - ECON 4109H LECTURE 5 Oligopoly...

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