Answer to Question #225488 in Economics of Enterprise for sulo

Question

a) The demand curve faced by monopolist and his total cost functions are given below; Demand function; Q = 3000 – 60P Total Cost function; TC = 100 +5Q+1/480Q2 a) Find profit Maximizing price and output level of this Monopoly firm.

b) Measure the firm profit margin at profit maximize output level.

c) “Compare to perfect competitive producer, the monopolist is misused scare resources” Explain using suitable grapes

Answer 1

Monopoly is a market form which has a sole seller or in other words, the monopoly competition has only one seller who produces unique products with no close substitutes for the same. The demand curve of the monopoly market is downward sloping as the monopolist engages in discriminating prices based on the different individuals or even markets and for this he sets the prices above the marginal costs.

a) The profit-maximizing price and output level of the monopoly firm can be calculated using the total cost and the total revenue function.

Calculating the total revenue function and then the marginal revenue:

$Q=3000-60P \\ 60P = 3000-Q \\ P= 50 - \frac{Q}{50} \\ TR=(50- \frac{Q}{50}) \times Q \\ TR=50Q- \frac{Q^2}{60} \\ MR=50-0.03Q$

Calculating marginal cost from Total cost function:

TC= 100+5Q+ \frac{Q^2}{480} \\

MC = 5 + 0.004Q

Calculating the equilibrium price and quantity:

50-0.03Q=5 + 0.004Q \\

50-5 = 0.03Q+0.004Q \\

45 = 0.034Q \\

Q= 1323.52 \\

1323.52 = 3000 -60P \\

60P= 3000-1323.52 \\

60P=1676.48 \\

P=27.94

b) For calculating the profit margin, the formula is revenue – cost/ revenue

$PM= \frac{36981-10367}{36981} \\ PM=0.719$

The firms can indulge in estimating their costs and revenue and also estimating the profit margin and can see the amounts of profits increased per total revenue.

c)

$P = \frac{3000 - Q}{ 60} \\ MC = \frac{dTC}{dQ} = 5 + \frac{2Q}{480} = 5 + \frac{Q }{ 240}$

A monopolist equates MR and MC.

$TR = PQ = \frac{3000Q - Q^2}{ 60} \\ MR = \frac{dTR}{dQ} = \frac{3000 - 2Q}{ 60} \\ \frac{3000 - 2Q}{ 60} = 5 + \frac{Q }{240} \\ 3000 - 2Q = 300 + \frac{60Q}{240} \\ 30000 - 2Q = 300 + \frac{Q}{4}$

Multiplying both sides by 4:

$12000 - 8Q = 1200 + Q \\ 9Q = 10800 \\ Q = 1200 \\ P = \frac{3000 - 1200}{ 60} = 30$

In perfect competition, P = MC, which maximizes total surplus.

$\frac{3000 - Q}{ 60} = 5 + \frac{Q }{ 240} \\ 3000 - Q = 300 + \frac{60Q}{240} \\ 30000 - Q = 300 + \frac{Q}{4}$

Multiplying both sides by 4:

$12000 - 4Q = 1200 + Q \\ 5Q = 10800 \\ Q = 2160 \\ P = \frac{3000 - 2160}{60} = 14$

So, monopoly price is higher and output is lower, compared to perfect competition, which implies a deadweight loss due to inefficient resource allocation and use.

In following graph, monopoly outcome is at point G where MR intersects MC, with price Pm and output Qm. Perfect competitive outcome is at point E where Demand intersects MC with price Pc and output Qc. The monopoly outcome causes a deadweight loss of EFG.