1. Assume a perfectly competitive constant cost industry, currently in long-run equilibrium. Market
demand in the industry is given by Q = 1500 - 25P. The short-run market supply curve is given by:
Q = 15P - 100 for P B 10
= 0 for P < 10
There are 25 firms in the industry.
(a) Calculate the equilibrium market price and quantity and the amount produced by each firm.
(b) Each firm is currently operating at the optimal plant size. What must be the minimum short-run average
variable costs for the firm and the efficient average cost? Explain
First, I don't know what you mean by "for P B 10" or "=0 for P<10"
That said, equilibrium will occur when Qd=Qs. You have the equations, simply solve for Q and then P. Hint: I get Q=500, P=40. Since there are 25 firms, Qi=500/25 = 20
b) since each firm is at it's optimal plant size, and the P and Q are at their long-run equilibriums, the firm must be operating where AVC=P.
Take a shot, explain why this must be so.
I hope this helps
(a) To calculate the equilibrium market price and quantity, we need to find the point where the market demand and supply curves intersect.
First, let's calculate the equilibrium price.
Set the market demand equation (Q = 1500 - 25P) equal to the market supply equation (Q = 15P - 100):
1500 - 25P = 15P - 100
Combine like terms:
40P = 1600
Divide both sides by 40:
P = 40
The equilibrium price is P = 40.
To find the equilibrium quantity, substitute the equilibrium price into either the market demand or supply equation. Let's use the market supply equation:
Q = 15P - 100
Q = 15(40) - 100
Q = 600 - 100
Q = 500
The equilibrium quantity is Q = 500.
Now, to find the amount produced by each firm, we divide the equilibrium quantity by the number of firms. In this case, there are 25 firms, so:
Amount produced by each firm = 500 / 25 = 20
Therefore, each firm produces 20 units.
(b) To find the minimum short-run average variable costs (SRAVC) for the firm and the efficient average cost, we need to look at the short-run supply curve.
The short-run supply curve for P < 10 is given as Q = 0. This means that firms are not willing to produce any quantity below a price of 10, as it would not cover their variable costs.
So, for the firm to start producing, the price should be at least 10. Thus, the minimum short-run average variable costs (SRAVC) for the firm would be the variable cost per unit when producing at a price of 10.
Using the short-run supply equation for P ≥ 10: Q = 15P - 100
When P = 10:
Q = 15(10) - 100
Q = 150 - 100
Q = 50
Therefore, the minimum short-run average variable costs for the firm would be the variable cost per unit at a quantity of 50, which can be calculated by dividing the total variable cost by the quantity.
The efficient average cost is the minimum average cost achievable in the long run when all factors of production can be adjusted. In a perfectly competitive constant cost industry, the efficient average cost is equal to the minimum short-run average cost curve (SAC) and is achieved when the firm is operating at its optimal plant size.
To calculate the efficient average cost, we need more information about the firm's technology and cost curves.