Answer to Question #221298 in Microeconomics for saraa

Question

Suppose the inverse demand for a monopolist’s product is given by P = 70-0.5Q. The monopolist can produce output in two plants. The marginal coat of producing in plant 1 is MC1 = 3Q1 and the marginal cost of producing in plant 2 is MC2 = Q2. How much output should be produce in each plat to maximize profit? And what price should be charged?

Compare to perfect competition, monopolist charged higher price and supply less quantity with long run firm equilibrium. Discuss using suitable graph.

Explain the deadweight loss of monopolization

Answer 1

Solving for multiple monopolists:

The given explanation about the prices (P) and marginal cost (MC) of individual firms:

$P=70 -0.5Q \\ MC_1=3Q_1 \\ MC_2= Q_2$

Now solving for marginal revenue (MR), the following equation can be obtained:

Total Revenue = $Price \times Quantity$

$TR = (70-0.5Q) \times Q \\ = 70Q-0.5Q^2$

Marginal Revenue $= \frac{∂TR}{∂Q} = 70 -Q$

As the MC for each firm is already given, now set $MC_1 = MC_2 = MC_T$ , so as to find out profit-maximizing prices and quantity:

$Q=Q_1+Q_2 \\ = \frac{MC_1}{3}+MC_2 \\ = \frac{MC_T}{3}+ MC_T \\ = \frac{4MC_T}{3} \\ MC_T= \frac{3Q}{4}$

Equating $MC_T$ with MR (both calculated above):

$MR=MC_T \\ 70-Q = \frac{3Q}{4} \\ Q=40 \\ MR=MC_T=30$

Similarly; the profit (Æ›) maximizing quantities.

$MC_1=3Q_1 \\ 30 = 3Q_1 \\ Q_1=10 \\ MC_2=Q_2 \\ Q_2=30$

Putting these in the dd curve equation to find out the price (P) charged by monopoly:

$P=70-0.5Q \\ P=70-0.5 \times 40 \\ P=70 -20 =50$

Solving for the perfect competition (PC):

Now instead of equating $MC_T$ with P, instead of MR:

$MC_T=P \\ \frac{3Q}{4} = 70 -0.5Q \\ Q=56 \\ P=42$

Profit (Æ›) maximizing quantities are calculated as follows:

$MC_1=3Q_1 \\ 42=3Q_1 \\ Q_1=14 \\ MC_2=Q_2=42$

So as comparing with the monopoly, both firms will be producing higher quantities even at lower prices when they behave as perfect competition (PC).

Part C) Showing this by using the graphs: Where

Red Curve: Average revenue

Blue Curve: Marginal revenue

Black Curve: Marginal cost

The monopoly pricing creates a deadweight loss because the firm forgoes transactions with the consumers. The deadweight loss is the potential gains that did not go to the producer or the consumer. A monopoly is less efficient in total gains from trade than a competitive market.