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

Question

Quizplus · Accepted Answer

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/U1P1S1
Substituting the given parameters, we get:
C(Y) = 9Y + 0.5P0 + 81/P1
The 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)Y
Simplifying,
60Y + P = 51Y^2
The equilibrium price and quantity are then found by solving this equation simultaneously with the demand curve:
51 - P = 51Y - Y^2
Rearranging,
Y^2 - 51Y + P - 51 = 0
Using the quadratic formula,
Y = (51 +/- sqrt(51^2 - 4P + 204)) / 2
To ensure a positive quantity, we take the positive root:
Y = (51 + sqrt(2601 - 4P)) / 2
Substituting into the demand equation,
P = 51 - (51 + sqrt(2601 - 4P)) / 2
Solving for P, we get:
P = 6
Substituting back into the expression for Y, we get:
Y = 15
Therefore, the equilibrium price is $6 and the equilibrium number of firms is 15. The answer is D.

Suppose That Each Firm Has the Cost Function C(y)= Y2

Suppose That Each Firm Has the Cost Function C(y)= Y²