Julee has estimated the demand and marginal revenue for her product. They are P = 100 − 2Q (quantity) and MR = 100 − 4Q, respectively. She also experiences constant marginal cost of $16.
a.Does Julee have any market power? How can you tell?
b.What is Julee’s profit-maximizing quantity?
a. To determine whether Julee has market power, we need to consider the relationship between her marginal revenue (MR) and marginal cost (MC). Market power refers to a firm's ability to influence market prices and outcomes. One way to assess this is by comparing the marginal revenue with the marginal cost.
In this case, Julee's marginal revenue function is MR = 100 - 4Q. Since the marginal revenue function is derived from the demand function, which is P = 100 - 2Q, we can equate MR to the price (P) to determine market power:
MR = P
100 - 4Q = 100 - 2Q
By rearranging this equation, we find:
-4Q + 2Q = 0
-2Q = 0
Q = 0
This implies that Julee's profit-maximizing quantity is when she produces zero units. However, this is not practically feasible. This indicates that Julee does not have market power because she cannot influence the market price.
b. The profit-maximizing quantity can be determined by equating marginal revenue (MR) with marginal cost (MC). Since we know the marginal cost is a constant $16, we can set up the equation:
MR = MC
100 - 4Q = 16
Rearranging this equation, we find:
-4Q = 16 - 100
-4Q = -84
Q = (-84)/(-4)
Q = 21
Therefore, Julee's profit-maximizing quantity is 21 units.