SectionWS13 - Exercise 2(Rent We consider rms that have...

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Econ 100A - Worksheet #13 Long Run Equilibrium Exercise 1 (Pollution on a Perfectly Competitive Market) We consider an industrial good that is produced with the following long run cost function. C ( q ) = q 3 10 - 3 q 2 + 40 q. The demand for the good is given by Q d ( p ) = 6075 - 90 p. 1. a) Compute and plot the average cost and marginal cost functions. b) Find the optimal number of firms that can operate on this market in the long run when the market is perfectly competitive. 2. The production technology of the good is polluting: for each unit of good produced, two ft 3 of carbon dioxide are released in the air. To fight this pollution, the Government imposes a tax of t dollars per unit produced. a) What is the new cost function? b) Compute the profitability threshold as a function of t . c) Find the optimal number of firms that can operate on this market in the long run when the market is perfectly competitive as a function of t . d) Find what value of the tax should be set so as to ensure that the volume of carbon dioxide is equal to G ft 3 in the long
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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 > 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 ) > 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 < 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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