Question

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 given by the MC equation. Use the optimality condition to show the demand elasticity of the monopoly, where |ε(y) | is the demand elasticity.

d. Under monopoly output would not be maximized when MR is negative. Use the elasticity expression to show why. Hint. In a competitive market, the firm faces a horizontal demand curve (i.e. infinitely elastic, |ε(y)|= ∞). Thus the optimality condition is just P= MC.

Answer #1

Assume the inverse demand curve a monopoly faces is p = 100 -
2Q, and MC is constant at 16.
Find the monopoly’s profit maximization output.
Find the monopoly’s profit maximization price.
Find the monopoly’s maximum profit.
Find the monopoly’s deadweight loss.
Please show work for parts c and d

Suppose the (inverse) demand function facing a firm is p(q)=10 –
q, where p is the price, q is quantity.
1. Draw the (inverse) demand function and marginal revenue. Show
your detailed work such as slope, intercept.
2. Suppose the firm has a marginal cost MC=q, and it is the only
firm in the market (that is, monopoly). Find the output level and
price set by the firm based on your graph in (1). (You do not need
to derive...

1) The inverse demand curve a monopoly faces
is
p=110−2Q.
The firm's cost curve is
C(Q)=30+6Q.
What is the profit-maximizing solution?
2) The inverse demand curve a monopoly faces
is
p=10Q-1/2
The firm's cost curve is
C(Q)=5Q.
What is the profit-maximizing solution?
3) Suppose that the inverse demand function for
a monopolist's product is
p = 7 - Q/20
Its cost function is
C = 8 + 14Q - 4Q2 + 2Q3/3
Marginal revenue equals marginal cost when output
equals...

Monopoly
Consider a monopoly facing an inverse demand function P(q) = 9 − q
and having a cost
function C(q) = q.
(a) Find the profit maximizing output and price, and calculate the
monopolist’s profits.
(b) Now, suppose the government imposes a per unit tax t = 2 to
the monopoly. Find the
new price, output and profits. Discuss the impact of that tax.

A monopolist faces an inverse demand of p(y)=100-5y, and its
total cost of production is c(y)=20y, where y is the output level.
The monopolist maximizes its profits at output level equal to 8.
Calculate the deadweight loss of this monopoly.

Consider the market for good Q. The inverse demand function is
p(Q) = 24 – 2Q, where p denotes the price of good Q. The production
costs of the representative firm are C(Q) = 4Q. In addition,
production causes environmental damage of D(Q) = 12Q.
a) Determine the socially optimal output level Q*. Discuss the
optimality condition and illustrate your solution in a
diagram.
b) Assume that there is no government intervention. Calculate the
market equilibrium in the case of...

A monopoly faces the following inverse demand function:
p(q)=100-2q, the marginal cost is $10 per unit.
What is the profit maximizing level of output, q*
What is the profit maximizing price
what is the socially optimal price
What is the socially optimal level of output?
What is the deadweight loss due to monopoly's profit maximizing
price?

A monopolist faces the inverse demand function p = 300 – Q.
Their cost function is c (Q) = 25 + 50Q. Calculate the profit
maximizing price output combination

1. Suppose a monopoly with a cost function of C(Q) = 0.5Q2 + 10Q
+ 392 faces a market demand of P = 500 – 17Q.
A) What is its profit maximizing level of output, what price
will it charge, and what will its profits be?
B) If we imposed a MC price ceiling on the monopoly, how much
would we need to subsidize them in order for them to remain in
business?
C) How much would the firm be...

Monopoly
Consider a situation where a monopolist faces the following
inverse market demand curve
p = 132 − 2q
and the following cost function
T C = 12q + 2q 2
f) How much deadweight loss does the monopolist create?
g) What could the government do to regulate the monopolist?

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