Assume that you have a market where the demand curve is P=100-4Q .Assume also that all firms produce the good using constant marginal cost function where MC=4, no matter how many units are produced.
To analyze the market in this scenario, we need to understand the demand and supply functions. The demand function is given as P = 100 - 4Q, where P represents the price and Q represents the quantity demanded.
1. First, let's find the market equilibrium price and quantity. At equilibrium, the quantity demanded is equal to the quantity supplied. In this case, since there is no information given about the supply curve, we assume it to be perfectly competitive, meaning it follows the marginal cost (MC) function.
2. The marginal cost (MC) function is given as MC = 4, which means that the cost of producing each additional unit is constant and equal to 4.
3. To find the equilibrium quantity, set the quantity demanded equal to the quantity supplied:
Quantity Demanded (Qd) = Quantity Supplied (Qs)
100 - 4Q = Qs (since MC = 4)
Rearranging the equation, we have: 4Q + Qs = 100
4. To find the equilibrium price, substitute the value of Qs back into the demand function:
P = 100 - 4Qs
5. Now we have two equations: 4Q + Qs = 100 and P = 100 - 4Qs. We can solve these simultaneous equations to find the equilibrium price and quantity.
6. Substitute the value of Qs from the first equation into the second equation:
P = 100 - 4Qs = 100 - 4(100 - 4Q) = 100 - 400 + 16Q = -300 + 16Q
7. Simplify the equation to find the equilibrium price:
P = -300 + 16Q
8. Now, substitute the value of P into the first equation:
4Q + Qs = 100
4Q + (P + 300)/16 = 100
Multiply both sides by 16:
64Q + P + 300 = 1600
9. Substitute P = -300 + 16Q into the equation:
64Q + (-300 + 16Q) + 300 = 1600
Simplify and solve for Q:
80Q = 1600
Q = 20
10. Now, substitute the value of Q into the equation for P:
P = -300 + 16Q
P = -300 + 16(20)
P = -300 + 320
P = 20
Therefore, the equilibrium price in this market is 20, and the equilibrium quantity is 20.