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2350 ch25 problem answer
Intermediate Microeconomic Theory II (York University)
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CHAPTER 25
Monopoly
TRUE/FALSE WITH EXPLANATION:
1.
Since a monopoly charges a price higher than marginal cost, it will
produce an inefficient amount of output.
2.
If the interest rate is 10%, a monopolist will choose a markup of price
over marginal cost of at least 10%.
3.
A natural monopoly occurs when a firm gains ownership of the entire
stock of some natural resource and thus is able to exclude other producers.
4.
If he produces anything at all, a profit-maximizing monopolist with
some fixed costs and no variable costs will set price and output so as to maximize
revenue.
5.
For a monopolist who faces a downward-sloping demand curve,
marginal revenue is less than price whenever quantity sold is positive.
6.
A monopolist with constant marginal costs faces a demand curve with
a constant elasticity of demand and does not practice price discrimination. If the
government imposes a tax of $1 per unit of goods sold by the monopolist, the
monopolist will increase his price by more than $1 per unit.
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ANSWER:
1. True. Efficient output level is where P = marginal benefit to consumer =
marginal cost. In other words, as long as consumer is willing to pay a
price for the marginal unit that is greater than the cost of producing the
unit, society would gain if more were produced. By charging a price
greater than marginal cost, monopolists produces less than the socially
efficient level.
2. False. Markup has nothing to do with interest rate. Mark up over
marginal cost is derived from the profit maximizing condition:
MR = P (1 + 1/e) = MC or P = MC/ (1 + 1/e) and P – MC = -MC/(1 + e),
where e = elasticity of demand.
3. False. A natural monopoly arises when the firm’s technology has
economies-of-scale large enough for it to supply the whole market at a
lower average total production cost than is possible with more than one
firm in the market
4. True. If variable cost is zero, so is marginal cost. Therefore, firm’s
profit-maximizing output is where, MR is also zero. At this point total
revenue is maximized.
5. True. Since whenever the monopolist sells a unit more, she must reduce
price along the downward sloping demand curve. This means that
monopolist’s total revenue will go up by the price of the additional unit
minus the revenue lost on all the previous units, which also must be sold
for the new lower price. Example: Monopolist is selling 10 units for a
price of $10. Total revenue is $100. To sell 11units monopolist must
reduce the price, say to $9.5. Total revenue now is 11 x 9.5 = $ 104.5.
Marginal revenue is $4.5 < $ 9.5.
6. True. Assume constant elasticity is e and constant marginal cost is k.
From the mark up expression we know that: P = k/(1 + 1/e). A tax will
raise marginal cost by the amount of the tax. Noting that k and e are
constant, differentiating the mark up expression:
dP/dk = 1/(1 + 1/e) > 1, since e < -1 (demand is always elastic at
monopolist’s profit maximizing output). Thus, price will rise by more
than $1 when the tax raises k by $1.
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MULTIPLE CHOICE:
1.
A monopolist faces the inverse demand function described by p = 50
− 4q, where q is output. The monopolist has no fixed cost and his marginal cost is
$5 at all levels of output. Which of the following expresses the monopolist’s profits
as a function of his output?
a.
50 − 4q − 5
b.
50 − 8q
c.
45q − 4q2
d.
50q − 4q2 − 5
e.
None of the above.
2.
A monopolist faces the inverse demand curve p = 64 − 2q. At what
level of output is his total revenue maximized?
a.
24
b.
26
c.
8
d.
32
e.
16
3.
A profit-maximizing monopolist faces the demand curve q = 100 −
3p. It produces at a constant marginal cost of $20 per unit. A quantity tax of $10
per unit is imposed on the monopolist’s product. The price of the monopolist’s
product
a.
rises by $5.
b.
rises by $10.
c.
rises by $20.
d.
rises by $12.
e.
stays constant.
4.
The demand for a monopolist’s output is 6,000/(p + 2)2, where p is the
price it charges. At a price of $3, the elasticity of demand for the monopolist’s
output is
a.
−1.
b.
−2.20.
c.
−1.20.
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d.
e.
−1.70.
− 0.70.
5.
The demand for a monopolist’s output is 6,000/p2, where p is its price.
It has constant marginal costs equal to $5 per unit. What price will it charge to
maximize its profits?
a.
$33
b.
$12
c.
$26
d.
$10
e.
$5
6.
A monopolist faces a constant marginal cost of $1 per unit. If at the
price he is charging, the price elasticity of demand for the monopolist’s output is −
0.5, then
a.
the price he is charging must be $2.
b.
the price he is charging must exceed $2.
c.
the price he is charging must be less than $2.
d.
the monopolist cannot be maximizing profits.
e.
the monopolist must use price discrimination.
7.
A monopolist has decreasing average costs as output increases. If the
monopolist sets price equal to average cost, it will
a.
produce too much output from the standpoint of efficiency.
b.
lose money.
c.
produce too little output from the standpoint of efficiency.
d.
maximize its profits.
e.
face excess demand.
8.
A monopolist produces at a point where the price elasticity of demand
is − 0.7 and the marginal cost is $2. If you were hired to advise this monopolist on
how to increase his profits, you would find that the way to increase his profits is to
a.
increase his output.
b.
lower the price.
c.
decrease his output.
d.
produce the output level where marginal cost equals price.
e.
increase his advertising efforts.
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9.
A natural monopolist has the total cost function c(q) = 350 + 20q,
where q is its output. The inverse demand function for the monopolist’s product is
p = 100 − 2q. Government regulations require this firm to produce a positive
amount and to set price equal to average costs. To comply with these requirements
a.
is impossible for this firm.
b.
the firm must produce 40 units.
c.
the firm could produce either 5 units or 35 units.
d.
the firm must charge a price of $70.
e.
the firm must produce 20 units.
10. A monopolist faces a downward-sloping demand curve and has fixed
costs so large that when she maximizes profits with a positive amount of output,
she earns exactly zero profits. At this positive, profit-maximizing output,
a.
there are decreasing returns to scale.
b.
demand is price inelastic.
c.
marginal revenue is greater than marginal cost.
d.
price equals marginal cost.
e.
average total cost is greater than marginal cost.
11. The demand for Professor Bongmore’s new book is given by the
function Q = 2,000 − 100p. If the cost of having the book typeset is $7,000, if the
marginal cost of printing an extra copy is $4, and if he has no other costs, then he
would maximize his profits by
a.
having it typeset and selling 800 copies.
b.
having it typeset and selling 1,000 copies.
c.
not having it typeset and not selling any copies.
d.
having it typeset and selling 1,600 copies.
e.
having it typeset and selling 400 copies.
12. A profit-maximizing monopoly faces an inverse demand function
described by the equation p(y) = 40 − y and its total costs are c(y) = 7y, where
prices and costs are measured in dollars. In the past it was not taxed, but now it
must pay a tax of 6 dollars per unit of output. After the tax, the monopoly will
a.
increase its price by 6 dollars.
b.
increase its price by 9 dollars.
c.
increase its price by 3 dollars.
d.
leave its price constant.
e.
None of the above.
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ANSWERS:
1. C. Profit = Total Revenue – Total Cost = pq - 5q or (50 -4q)q – 5q
2. E. MR = 64 -4q = 0, or q = 16. At maximum revenue, MR =0.
3. A. For linear demand function, MR is twice as steep as the demand
function. If MC is constant, then profit maximizing price must rise
by half the increase in MC due to a tax.
4. C. Elasticity, e = (p/q)dq/dp. At p =3, q = 6000/125 = 240, p/q = 1/80
And
dq/dp = -2(6000)/(p + 2)3 = -1200/125 = -96. Therefore, e = -96/80 = 1.2
5. D. For demand functions of the form q = Ap-x, where A and x are
constants, elasticity is always -x. So here e = -2. Therefore, P = MC/(1
+ 1/e) = 5/(1 – ½) = 10.
6. D. When e > -1 (such as here, -.5 > -1), demand is inelastic and MR is
negative. So, the monopolist should reduce output to raise revenue,
reduce cost and increase profit.
7. C. Monopolist sets MR = MC to maximize output. MR is always less
than price. Therefore, P > MC. For efficiency, we need P = MC.
Therefore, monopolist should expand output and reduce price for
efficiency.
8. C. Same as 6.
9. C. AC = c/q = 350/q + 20. Therefore, P = 100 -2q = 350/q +20. Solve
for q from this quadratic function 100q -2q2 = 350 +20q or q2 - 40q
+175 = 0. Check the roots are, 5 and 35.
10. E. Zero profit at the profit maximizing output implies p = AC.
Therefore, at the profit maximizing output, AC must be tangent to
the downward-sloping demand line. Since AC must be declining at
this point, MC must be below AC.
11. C. If he produces, maximum profit will be where MR = MC. From
the inverse demand function, p = 20 – 1/100Q, MR is 20 – 1/50Q.
Setting MR = 20 – 1/50Q = MC = 4, Q =800 and p = 12. Total
Revenue = pQ = 9600 and total cost = 7000 + 4 x 800 = 10200. Since,
TC > TR should not produce.
12.
C. Same as 3.
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