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Unformatted text preview: Exercise 2 (Rent) We consider rms that have dierent costs functions: rm of type k , k = 1 , 2 ,... has the following long run cost function. C k ( q ) = 3 q 2 + k if q &gt; if q = 0 , 1. Let q e k be the minimum ecient scale of a rm of type k and t k its protability threshold. Find their value for each k . 2. Determine the competitive supply function of a type k , denoted q * k ( p ) . 3. The demand is given by: D ( p ) = 30- p 2 3 . We assume that there is only one rm of each type. a) Explain economically why the optimal number of rms in the long run is the number k * , the largest k such that: D ( s k ) &gt; q * 1 ( t k ) + q * 2 ( t k ) + ... + q * k-1 ( t k ) + q e k . b) Find k * . c) Find the long run equilibrium price, the quantity produced by each rm and its prot. d) Why can we say that if k &lt; k * , the type k rm enjoys a rent? Compute the value of this rent for each of the relevant rms. 1...
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- Fall '08