Consider a natural monopoly with market demand
P = 100 – 10Q
and whose total cost curve and...

Question

Consider a natural monopoly with market demand
P = 100 – 10Q
and whose total cost curve and marginal cost curve can be expressed as
TC = 100 + 20Q + Q2 
MC = 20 + 2Q
a. Write an equation for this natural monopoly’s average total cost (ATC) curve?
b. Using the equation you wrote in (a) fill in the following table.




Q


ATC




1







2







4







5







10







20







c. Draw a graph of this firm’s demand curve, ATC curve, and MC curve. At what (Q, P) do MC and ATC intersect one another? Show how you found there coordinates. Is this (Q, P) pair a likely equilibrium in this market? Explain your answer fully.
d. Suppose this monopolist acts as a single price profit maximizing monopolist. Determine the monopolist’s price, quantity, and profit with this scenario. Round your answers to the nearest hundredth.
e. Suppose this monopolist is regulated to produce the socially optimal amount of output (where P = MC for the last unit produced and sold). Given this regulatory decision, determine the monopolist’s price, quantity, and profit. Round your answers to the nearest hundredth.
f. Suppose this monopolist is regulated to produce that quantity where profit is equal to zero. Given this regulatory decision, determine the monopolist’s price, quantity, and profit. Round your answers to the nearest hundredth.

Robert · Accepted Answer

Answers: 
a. ATC = (100/Q) + 20 + Q 
b.  
Q ATC 
1 $121 per 
unit 
2 72 
4 49 
5 45 
10 40 
20 45
c. ATC = MC 
(100/Q) + 20 + Q = 20 + 2Q 
(100/Q) = Q 
Q = 10 units of output 
MC = 20 + 2Q 
MC = 20 + 2(10) = 40 
P = $40 per unit of output 
(Q, P) = (10 units of output, $40 per unit of output) 
This point lies to the right of the demand curve and will therefore not be a likely (Q, P) 
equilibrium in this market since at a price of $40 per unit, there is only demand for 6 
units of output. Or, at a quantity of 10 units, demanders willingness to pay can be 
calculated as $0 per unit of output.  
 
d. MR = 100 – 20Q 
MC = 20 + 2Q 
MR = MC determines the single price monopolist’s optimal quantity. So,  
100 – 20Q = 20 + 2Q or Q = 3.64 units of output 
Use the demand curve to find the price the monopolist should charge for this level of 
output: P = 100 – 10Q = 100 – 10(3.64) = $63.60 per unit of output 
Profit = TR – TC  
TR = P*Q = ($63.

Consider a natural monopoly with market demand P = 100 – 10Q and whose total cost curve and marginal cost curve can be expressed as TC = 100 + 20Q + Q 2 MC = 20 + 2Q a. Write an equation for this...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment