suppose that each firm has the cost function c(y)  y²  9 for y  0 and c(0)  0.With industry demand given by D(p)  51  p, the equilibrium price and equilibrium number of firms in the industry (in that order) will be

A) $8 and 11.
B) $3 and 18.
C) $3 and 48.
D) $6 and 15.
E) $6 and 45.

Question

Hashim Muhammed · Accepted Answer

Final Answer : D, Explanation :  To find the equilibrium price and number of firms, we need to solve for the intersection of the industry demand and the total industry cost curves. The total industry cost curve is the sum of each firm's cost curve, which in this case is given by:C(Y) = (F1/S1)Y + F1P0/S1 + F1^2/U1P1S1Substituting the given parameters, we get:C(Y) = 9Y + 0.5P0 + 81/P1The industry supply curve is then given by setting the total cost equal to the industry revenue (price times quantity):9Y + 0.5P0 + 81/P1 = (51 - P)YSimplifying,60Y + P = 51Y^2The equilibrium price and quantity are then found by solving this equation simultaneously with the demand curve:51 - P = 51Y - Y^2Rearranging,Y^2 - 51Y + P - 51 = 0Using the quadratic formula,Y = (51 +/- sqrt(51^2 - 4P + 204)) / 2To ensure a positive quantity, we take the positive root:Y = (51 + sqrt(2601 - 4P)) / 2Substituting into the demand equation,P = 51 - (51 + sqrt(2601 - 4P)) / 2Solving for P, we get:P = 6Substituting back into the expression for Y, we get:Y = 15Therefore, the equilibrium price is $6 and the equilibrium number of firms is 15. The answer is D.

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suppose that each firm has the cost function c(y)  y2  9 for y  0 and c(0)  0.With industry demand given by D(p)  51  p, the equilibrium price and equilibrium number of firms in the industry (in that order) will beA) $8 and 11.B) $3 and 18.C) $3 and 48.D) $6 and 15.E) $6 and 45.

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