Question

Microeconomics:

SG Express has a monopoly on shipping delivery in a local community. The demand for SG Express is Q = 600 – 5P.

SG Express' cost of providing shipping delivery is C = 200 +
Q^{2}

a. What are the profit-maximizing price and output level? What is the profit? Show your workings.

b. Find the Lerner Index of SG Express. Show your workings.

c. Use the result to (b), estimate the price elasticity of demand. Show your workings.

Answer #1

a) Q = 600 - 5P

5P = 600 - Q

P = 120 - 0.2Q (this is inverse demand function)

TR = P * Q = 120Q - 0.2Q^{2}

MR = 120 - 0.4Q

TC = 200 + Q^{2}

MC = 2Q

The profit maximization condition is

MR = MC

120 - 0.4Q = 2Q

2.4Q = 120

Q = 120 / 2.4 = 50

P = 120 - 0.2(50) = $110

TR = P * Q = $110 * 50 = $5,500

TC = 200 + (50)^{2} = $2,700

Profit = TR - TC = $5,500 - $2,700 = $2,800

Thus, the profit maximizing price is $110, output is 50 and profit is $2,800.

b) P = $110

MC = 2Q = 2 * 50 = $100

Lerner Index = (P - MC) / P

= (110 - 100) / 110

= 0.091

c) we know, the Lerner index is equal to the inverse of the elasticity in its absolute value

Learner Index = 1 / |E|

0.091 = 1 / |E|

|E| = 1 / 0.091 = 10.99

Thus, the elasticity is 10.99

McCullough has a monopoly on rental dwellings in the local
community. The demand function for rental dwellings is Q = 70,000 -
50P. McCullough's total cost of providing rental dwellings is TC =
0.005Q2 + 20Q
a. What price will this monopolist charge? What quantity will it
sell? How much profit does McCullough make? (8 points)
b. What would output be if DD acted like a perfect competitor
and set MC = P? What profit would then be generated? (6...

This is a price setting firm problem.(show all work)
Demand Function: P=32-Q
Total Cost Function: C=Q²+8Q+4
Profit maximizing price is.....?
Profit maximizing quantity is......?
Profit is......?
Lerner Index Value is......?
Price Elasticity of Demand is......?
To maximize sales, this firm would change a price...... and sell
a quantity of..........?

You are a monopolist with the following demand and cost
conditions:
Q = 50 - .5P and
C(Q) = 50 + Q2.
a. Determine the profit-maximizing output and price.
b. Show your total revenue, total cost and profits.

Monopoly, markup formula, Lerner index, deadweight loss]
Megasoft makes a word-processing program. Marginal cost of
producing the program is $10. The elasticity of demand for the
program is ε = -1.5.
a. What price should Megasoft charge for the program, to
maximize profit? $
b. Compute the Lerner index (also called the "price-cost margin"
or the "markup ratio") for this monopolist. Recall that the Lerner
index is defined as L = (P-MC) / P . L =
c. Compute social...

A monopolist has the following cost function C(q) = 2000 + 40q.
The demand for its product is given by: q = 100 ? p/2.
(a) Find the optimal quantity, price, and profit.
(b) Find the elasticity of demand at the monopoly quantity and
the Lerner index.
(c) Find the dead-weight loss due to the monopoly.

The manager of a local monopoly estimates that the elasticity of
demand for its product is constant and equal to -3. The firm’s
marginal cost is constant at $35 per unit.
a. Express the firm’s marginal revenue as a function of its
price.
Instruction: Enter your response rounded to two
decimal places.
MR = ____________________ × P
b. Determine the profit-maximizing price.
Instruction: Use the rounded value calculated
above and round your response to two decimal places.
$ __________________________

3. Jamie Co. has a patented disinfectant to clean the
kitchen of restaurants. The market demand for her patented
disinfectant is Q = 1,000 – 0.2P. Jamie Co. has a total cost
function of C = 100,000 + 2,000Q + 10Q2 . What is the
profit-maximizing price and output level of Jamie Co.? Show your
workings.

Daisy Duck has a monopoly in oil refinement in the local market.
The demand for Daisy’s oil is: P = 65 - q.The relevant marginal
revenue function is MR(q) = 65 - 2 · q. Her marginal cost function
is MC(q) = 8. In the refinement of oil, she emits pollution that
has the marginal external cost function: MEC(q) = 2. What level of
output will Daisy select to maximize profits? What is the marginal
social cost of Daisy’s profit?...

. A town has a monopoly supplier of potable water. The
monopolist faces the following demand, marginal revenue, and
marginal cost curves:
Demand: P = 70 – Q
Marginal Revenue: MR = 70 – 2Q
Marginal Cost: MC = 10 + Q
Graph these curves.
Assuming that the firm maximizes profit, what quantity does it
produce? What price does it charge? Show these results on your
graph.
The local government decides to impose a price ceiling that is
10 percent...

A monopolist faces a demand curve P= 24 – 2Q, where P is
measured in dollars per unit and Q in thousands of units and MR=24
– 4Q. The monopolist has a constant average cost of $4 per unit and
Marginal cost of $4 per unit. a. Draw the average and marginal
revenue curves and the average and marginal cost curves on a graph.
b. What are the monopolist’s profits-maximizing price and quantity?
c. What is the resulting profit? Calculate...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 9 minutes ago

asked 15 minutes ago

asked 16 minutes ago

asked 22 minutes ago

asked 28 minutes ago

asked 37 minutes ago

asked 39 minutes ago

asked 52 minutes ago

asked 53 minutes ago

asked 57 minutes ago

asked 58 minutes ago