Suppose that the market demand for a product is given by $Q_{D}=D(P)=A-B P$. Suppose also that the typical firm's cost function is given by $C(q)=k+a q+b q^{2}$ a. Compute the long-run equilibrium output and price for the typical firm in this market. b. Calculate the equilibrium number of firms in this market as a function of all the parameters in this problem. c. Describe how changes in the demand parameters $A$ and $B$ affect the equilibrium number of firms in this market. Explain your results intuitively. d. Describe how the parameters of the typical firm's cost function affect the long-run equilibrium number of firms in this example. Explain your results intuitively.
Added by Pedro V.
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In the long-run equilibrium, the price equals the minimum average cost. The average cost is given by $AC(q) = C(q)/q = k/q + a + bq$. The minimum average cost is found by taking the derivative of the average cost with respect to $q$ and setting it equal to zero. Show more…
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