Question

The following equations represent the function of total cost of a monopoly and the demand for a product made by the monopoly.

c = (1/12)q^{3} - (5/2)q^{2} + 30q + 100

q = 25 - p

a. Obtain the equation for revenue (r) coming from the sales of the product expressed in fonction of the quantities produced (q)

b. Obtain the equation for profits (?)

c. Obtain the level of production q* that would maximize the profits of the monopoly. Verify that at the level of production q = q*, the profits are maximized. What is the highest level of profits under which this business can aspire?

Answer #1

Cost function is c = (1/12)q3 - (5/2)q2 + 30q + 100.

Inverse demand function is p = 25 - q

a. Revenue function r = pq = (25 - q)q = 25q - q^2.

b. For the profit function we use ? = r - c (revenue - cost)

= 25q - q^2 - (1/12)q3 - (5/2)q2 + 30q + 100)

c. Profit is maximized when its derivative with respect to q is zero

d?/dq = 0

25 - 2q - (3/12)q^2 + (10/2)q - 30 = 0

-5 + 3q -q^2/4 = 0

q^2 -12q + 20 = 0

This gives q = 10 or q = 2. At q = 10, profit/loss = -83.33 and at q = 2, it is -104.67

Hence loss is minimized when q = 10. It is equal to -83.33

10. The demand for milk and the total costs of a dairy are
specified by the following equations:
P(Q) = 100 − Q
TC(q) = 30q
(a) Suppose there is a monopoly in the industry. Derive an
equation for marginal revenue of the monopolist. Graph the demand
and marginal revenue curves.
(b) Derive the marginal cost (MC) and average cost (AC) of milk
production. Graph MC and AC on the same graph as (a).
(c) Show the monopoly’s profit-maximizing price...

Consider the following total cost function for an individual
firm:
C(q) = 10+ q + (1/4)q^2
The industry demand is estimated to be:
Q = 100 - P
1) Now suppose there is a monopolist facing the industry demand.
Write down the monopolist's pro t function.
2) What is the equation of the monopolists marginal revenue
function? Also, explain how the monopolist's marginal revenue
function differs from the marginal revenue function of a firm in a
long-run perfectly competitive market....

1. You are the manager of a monopoly and your cost function is
C(Q) =2Q. You need to determine the optimal level of
output for your firm, but the demand for your firm’s product will
depend on whether or not a new tax law is passed. If passed, the
new tax law will reduce income taxes and increase consumers’
disposable income. Politicians have determined that there is a 70%
chance that the tax law will be passed and a 30%...

the
demand equiation of a goof is given by P+2Q=20 abd the total cost
function is Q3-8Q^2+20Q+2
a) find the level of output that maximizes total revenue
b) find the maximum profit and the value of Q at which it is
achieved. verify that, at this value of Q, MR=MC

1. A monopoly is best defined as a firm doing which of the
following?
A. Selling a product for which there are no close
substitutes
B. Making short-run economic profits
C. Having a degree of market power
D. Having a downward-sloping demand curve
2.What is assumed to be the monopoly firm’s underlying
objective?
A. To charge the highest price possible
B. To produce as little as possible
C. To maximize profits
D. To force competition out of business
3. When...

1. Consider a basic monopoly model where: The Inverse demand
p=P(q) & Cost function is c(y).There is a single uniform price
to all consumers.Use algebraic expressions to answer all of the
following for question 1.
a. What is the monopoly’s problem?
b. Given the cost function and the inverse demand equations set
up the first order condition. Solve the first order condition and
outline the monopoly’s pricing rule?
c.The total change in revenue that follows an increase in output
is...

The demand equation and average cost function of a manufacturing
firm are given by 200 = p+4q and AC = 0.8q^2 + 4 + (25/q)
respectively, where q is the number of units produced. Using the
information provided above, please answer the following questions
(a) Determine the amount of profit when it is maximized. (b)
Determine the amount of average cost at which maximum profit
occurs. (c) Determine the marginal cost of the product when profit
is maximized? (d) Given...

The equations for the demand and supply curves for a particular
product are P = 10 - .4Q and P = 2 + .4Q respectively, where P is
price and Q is quantity expressed in units of 100. After an excise
tax is imposed on the product the supply equation is P = 3 + .4 Q.
a- Compute equilibrium price and quantity before and after tax.
b-Calculate government's revenue from this tax. C- Calculate share
of producers and consumers...

A monopolist facing a market demand Q = 240 – 2p has the total
cost function TC(q) = q2. Draw carefully the relevant
graph with MC, MR, D curves and identify all relevant points,
intersections, intercepts.
(a) What is the monopolist’s profit maximizing quantity and
price?
(b) If the market is reorganized as perfectly competitive, what
should be the market price and quantity?
(c) Calculate the DWL associated with the monopoly in (a).
Now the government notices that the monopolist...

Toyota produces a certain aftermarket part for their vehicle
line with the following estimated demand function,
Q=140,000-12,000P Q is quantity demanded per year and P is price
charged. Toyota was able to say their fixed costs for this product
are $11,000 and variable costs are $1.75 per unit. A. Write the
total revenue function. B. Determine the marginal revenue. C. Write
the total cost function. D. Solve for marginal cost. E. Write an
equation for total profits. At what price...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 4 minutes ago

asked 28 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 55 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago