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Unformatted text preview: of pricetaking behavior is inconsistent.
Equilibrium must involve large firms with market power. General equilibrium with two goods: Y  CRS, X  IRS
Assume Y = Ly , Lx = fc + mcX and that 7 L = Lx + Ly Figure 11.2 For a given amount of X output, the minimum price which allows a
monopoly producer to break even is average cost, ac. (11.2) This is shown in Figure 11.2 by a cord connecting the production point A to
the Y intercept of the production frontier. Imperfect Competition 8 1. Derive the marginal revenue function for a monopolist
2. Show the relationship between the monopoly equilibrium and a
production tax for a closed economy. Marginal Revenue: The revenue derived from selling one more unit. For a
perfectly competitive firm, marginal revenue = price (since price is
fixed from the firm's point of view). For a monopolist, price must be lowered on all units in order to sell more.
So marginal revenue is less than price: price  loss of revenue on other
sales. 9
Revenue for a Cournot firm i and selling in country j is given by the price in
j times quantity of the firm’s sales. Price is a function of all firms’
sales. where Xj is total sales in market j
Cournot conjectures imply that (11.3) ; that is, a oneunit increase in the firm’s own supply is a oneunit increase in market supply.
Marginal revenue is then given by the derivative of revenue in (11.3) with
respect to firm i’s output (sales) in j. since (11.4) 10
Now multiple and divide the righthand equation by total market supply and
also by the price. (11.5) The term in square brackets in (11.5) is just the inverse of the price
elasticity of demand, defined as the proportional change in market
demand in response to a given proportional change in price.
This is negative, but to help make the markup formula clearer we will
denote minus the elasticity of demand, now a positive number, by the
Greek letter 0 > 0. We can then write (11.5) as 11 (11.6)
The term Xij/Xj in (11.6) is just firm i’s market share in market j, which we
can denote by sij . Then marginal revenue = marginal cost is given by: (11.7) Marginal revenue in Cournot competition turns out to have a fairly simple
form as shown in (11.7). The term
is referred to as the “markup”. 12
ProCompetitive Gains from Trade: Consider first autarky, and assume
one X producer in each of two identical countries.
In equilibrium, producers in both sectors equate marginal revenue to
marginal cost (marginal cost in Y equals price). This looks very much like a production tax on X. Closed economy
equilibrium with the X sector monopolized.
Figure 11.3: autarky equilibrium at point A, utility level Ua. Figure 11.3 Figure 11.4 Y Y Y pa Y1 Ua
p* U* exit Y p*=ac* ` U* ` Y A Ua 0 T A T
p=ac X X 13
Now allow free trade between the two identical countries: Figure 11.3. Trade leads to an expansion in X output and a fall in price for
both identical countries. Trade production/consumption at T. The average cost of producing X falls, improving producti...
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This document was uploaded on 03/09/2014 for the course ASTRO 3730 at Colorado.
 Winter '14
 PHILARMITAGE

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