Question

In: Economics

Question 1: Monopoly A monopoly’s demand function is given by: D;P=160-2Q. It’s costs are given by:...

Question 1: Monopoly

  1. A monopoly’s demand function is given by: D;P=160-2Q. It’s costs are given by: AC=MC=40. Calculate the firm’s profit.
  2. Based on a. illustrate this market, including all intercepts, and calculate the deadweight loss caused by the monopolisation of this market.
  3. The profit function for a second monopoly is given by: π=600Q-2Q3-1000. Calculate the firm’s fixed costs.
  4. Using the profit function in c. calculate the firms profit if it firm produces 17 units.
  5. Using the profit function in c. calculate the quantity of units this firm should produce in order to maximise profit.

Solutions

Expert Solution

(a) Given demand function is P = 160-2Q and AC=MC=40

So, the total revenue function is TR = P*Q = 160Q-2Q2 , and marginal revenue function is MR = dTR/dQ = 160-4Q

Total cost function is TC = AC*Q = 40Q

The profit of the monopoly is given by:

π = TR - TC = 160Q-2Q2-40Q = 120Q-2Q2

Profits are maximised at a point where dπ/dQ = 0 or MR = MC

Thus, 120-4Q = 0 or 160-4Q = 40

So, Qm = 30 and Pm = 160-2(30) = 100

and π = (120*30)-[2(30)2] = 3600 - 1800 = 1800

Qm = 30 , Pm = 100 and π = 1800.

(b) The monopoly in part (a) is shown below:

The monopoly equilibrium is depicted by em and perfect competition equilibrium is denoted by ec. The shaded triangle Aemec shows the deadweight loss (DWL) due to monopoly.

In perfect competition, P=MC

160-2Q=40

Qc = 60 and Pc = 40

Thus, DWL = area of triangle Aemec

= (1/2) * (Qc-Qm) * (Pm-Pc)

= (1/2) * (60-30) * (100-40) = (1/2)*30*60 = 900

DWL = 900

(c) Given that profits are  π = 600Q-2Q3-1000

We know that π =TR-TC

The only constant term in the profit is '1000' that is it is not dependent on the quantity sold. Thus, these are the total fixed costs which the monopolist has to bear even if it is not producing any output.

TFC = 1000

(d) When Q=17

π = 600Q-2Q3-1000

= (600*17) - [2(17)3] - 1000

= 10200 - 9826 - 1000

= -626

Thus, at Q=17 units the monopolist is incurring a loss of 626.

π = -626

(e) To maximise the profits, the firt should produce at a point where

dπ/dQ = 0  

d(600Q-2Q3-1000)/dQ = 0

600 - 6Q2 = 0

Q2 = 100

Q = 10

Thus, the monopolist should produce 10 units to maximise its profits.

Q = 10 units.


Related Solutions

A monopoly faces the following demand function: P=1200-Q. Variable production costs are VC(Q)=2Q^2.
A monopoly faces the following demand function: P=1200-Q. Variable production costs are VC(Q)=2Q^2. The firm also pays $50000 in costs that do not depend on production (even if q=0).What are the sunk costs, the fixed (but not sunk) costs, and the variable costs for this firm?Find the profit maximizing quantity and price, as well as profits.Repeat question 1 above if the costs of the firm are now 0 if it does not produce, but 2Q^2+150000 if it produces any positive...
A firms demand function for a good is given by P = 107-2Q and their total cost function is given by
A firms demand function for a good is given by P = 107-2Q and their total cost function is given by TC = 200+3Q . i). Obtain an expression for total revenue profit in terms of Q ii).  For what values of Q does the firm break even. iii). llustrate the answer to (ii) using sketches of the total cost function, the total revenue function and the profit function. iv). From the graph estimate the maximum profit and the level...
5.  A monopoly company faces the demand curve given by the equation P = 300 - 2Q....
5.  A monopoly company faces the demand curve given by the equation P = 300 - 2Q. Its production process is characterized by the total cost function TC=4Q2. The company charges a single price in the market. a. What is the marginal cost (as a function of output Q)? b. What is the total revenue (as a function of output Q)? c. What is the marginal revenue (as a function of output Q)? d. What levels of output and price would...
The (inverse) demand for vitamin D dietary supplement is p = 85−2q and the cost function...
The (inverse) demand for vitamin D dietary supplement is p = 85−2q and the cost function for any firm producing vitamin D is TC = (5q+F),where F is fixed cost. (a) What is a marginal cost? How much of vitamin D would a monopolist produce? What price would it charge? How much profit would it earn? (b) For which of the following values of F is a market for vitamin D a natural monopoly? F= $100, F= $200, F= $300,...
1. In the market for pencils, demand is given by P = 16 – 2Q, and...
1. In the market for pencils, demand is given by P = 16 – 2Q, and quantity supplied is given by P = 4 + Q. If the government provides a $3-per-unit subsidy to pencil producers, the cost of the subsidy to the government will be a. 12 b. 15 c. 6 d.3 e. None of these 2. In the market for pencils, demand is given by P = 16 – 2Q, and quantity supplied is given by P =...
Given the demand function Qd = D(p, y0), which is a function of price p and...
Given the demand function Qd = D(p, y0), which is a function of price p and exogenous income y0, the supply function Qs = S(p). Suppose both the D,S functions are not given in specific forms but possess continuous derivatives, if we know that supply function is strictly increasing, and demand function is strictly decreasing w.r.t price but a strictly increasing w.r.t income. (a) Write the equilibrium condition in a single equation. (b) Check whether the implicit-function theorem is applicable,...
A monopoly has an inverse demand function given by p = 120 - Q and a...
A monopoly has an inverse demand function given by p = 120 - Q and a constant marginal cost of 10. a) Graph the demand, marginal revenue, and marginal cost curves. b) Calculate the deadweight loss and indicate the area of the deadweight loss on the graph. c) If this monopolist were to practice perfect price discrimination, what would be the quantity produced? d) Calculate consumer surplus, producer surplus, and deadweight loss for this monopolist under perfect price discrimination.
A good’s demand is given by: P = 795 – 2Q. At P = 138, the...
A good’s demand is given by: P = 795 – 2Q. At P = 138, the point price elasticity is: Enter as a value (round to two decimal places if necessary).
1. In the Australian market for tea, demand is given by P = 10 - 2Q...
1. In the Australian market for tea, demand is given by P = 10 - 2Q and supply is P = 2Q. Q represents tonnes of tea per year. Suppose that the government provides a subsidy of $2 per ton of tea. The introduction of the subsidy will _______ consumer surplus by ________. 2. In the Australian market for coffee, demand is given by P = 10 - Q and supply is P = Q. Q represents tonnes of coffee...
1. Suppose that weekly demand for coal is given by P = 1800 – 2Q, and...
1. Suppose that weekly demand for coal is given by P = 1800 – 2Q, and supply is given by P = 4Q, where Q represents tonnes of coal. To support consumers, the government has decided to impose a price ceiling of $800 per tonne. This suggests that _________ of _________ will result in this market. Following the price ceiling, consumer surplus will _______ by_______. 2. In the Australian market for tea, demand is given by P = 10 -...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT