Assume that there are 1000 identical firms each with the marginal cost function of MC=10 + 2Q and the market demand function for the product is also given as P=1900-0.001Q, find the equilibrium of a firm in the market.

Answer 1

To find the equilibrium of a firm in the market, we need to use the following steps:

1. Set the marginal cost equal to the market price to get the optimal quantity for the firm:

MC = P
10 + 2Q = 1900 - 0.001Q
Solving for Q:
2.001Q = 1890
Q = 944.03

2. Plug the optimal quantity in the demand function to get the market equilibrium price:

P = 1900 - 0.001Q
P = 1900 - 0.001(944.03)
P = 1891.06

3. To check if this is a competitive equilibrium, we need to verify that each firm is making a profit at this price and quantity.

Total revenue for each firm:
TR = P x Q
TR = 1891.06 x 944.03
TR = 1,785,601.98

Total cost for each firm:
TC = MC x Q
TC = (10 + 2Q) x Q
TC = (10 x Q) + (2 x Q^2)
TC = (10 x 944.03) + (2 x 944.03^2)
TC = 1,889,310.56

Profit for each firm:
π = TR - TC
π = 1,785,601.98 - 1,889,310.56
π = -103,708.58

Since the profit is negative, each firm is not making a profit at this price and quantity. Therefore, this is not a competitive equilibrium and the market needs to adjust to a lower price or less output to reach a stable equilibrium.