LTC=2q-2q^2+q^3
Demand p=100-q
Determine the long run equilibrium
Price
Representative firm's output(q)
Industry output q and number of firm's in the industry
Student
University student
Economist
To determine the long-run equilibrium in this scenario, we need to find the intersection of the demand and supply curves in the industry.
1. Start by finding the long-run equilibrium price:
- Demand curve: p = 100 - q
- Supply curve is represented by the cost function: LTC = 2q - 2q^2 + q^3
To find the equilibrium price, set the quantity demanded equal to the quantity supplied:
100 - q = 2q - 2q^2 + q^3
Now, we solve this equation to find the equilibrium quantity, which we'll call q*.
2. Find the representative firm's output (q*):
- Once we find the equilibrium quantity (q*), we can substitute it back into either the demand or supply equation to find the price.
Since we want to determine the representative firm's output, we substitute q* into the supply equation:
LTC = 2q - 2q^2 + q^3
Substitute q* for q in the equation.
3. Find the industry output (Q) and the number of firms in the industry (n):
- The industry output (Q) is the total quantity supplied by all firms in the industry.
- The number of firms in the industry (n) is the total number of identical firms operating in the industry.
To find the industry output and number of firms, we need the market demand curve.
Since the market demand curve is p = 100 - q, substitute the equilibrium quantity (q*) into the market demand equation and solve for the market output (Q):
Q = 100 - q*
To find the number of firms (n) in the industry, you need additional information about the market structure, such as the market share of each firm or the market concentration ratios.