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Use Equation 2.5, the estimated supply function for
avocados, Q = 58 + 15p - 20pf, to determine how
much the supply curve for avocados shifts if the
price of fertilizer rises by $1.10 per lb. illustrate this
shift in a diagram.
Holding the price of fertilizer constant, by how
much would the price of avocados need to rise to
cause an increase of 60 million lbs per month in the
quantity of avocados supplied?
A firm should shut down only if it can reduce its loss by doing so. A firm cannot reduce its loss by shutting down if revenue is greater than the avoidable cost of production (or, in a competitive market, if price is greater than the average variable cost of production).
- Initially, the firm should not shut down because marginal
- revenue or price, which is $20, is greater than average variable cost, which is
- If average variable cost increases by $3 at every unit, then
- average cost increases by $3 at every unit. Now, the firm should shut down because the price of $20 is less than the average variable cost of $21.
A firm shuts down only if
- it can reduce its loss by doing so. That is, the firm shuts down
- only if its revenue is less than its avoidable variable cost. This is because if the firm shuts down, it does not incur the variable cost, so its only loss is its unavoidable fixed cost.
- In the first case, revenue is greater than variable cost, so
- the firm should not shut down to minimize losses.
- In the second case, revenue is less than variable cost, so the
- firm should shut down to minimize losses.
- In the third case, avoidable costs are $1,100, which are
- greater than revenue, so the firm should shut down.
Q = 58 + 15p - 20pf,
The firm’s profit is...
π = pq – (10 + 10q + q2).
- To find the profit-maximizing output level, take the derivative
- of the profit function with respect to q, set the derivative equal to zero, and then solve for q. The profit-maximizing quantity is
q = (p-10)/2
If p = 50, then q = 20. Note that the firm should indeed produce because it is profitable, with profit of $390.
In the long run, the average cost curve will
- shift down by the amount of a per-unit subsidy, and the firm’s marginal cost curve, or supply curve, will shift right. Because the market price will not change significantly with lower costs for one firm, the firm will increase its output to where its new marginal cost equals market price, and its profits will go
- from the market equilibrium of zero to a positive amount.
If the inverse demand function is p = 300 - 3Q,
what is the marginal revenue function? Draw the
demand and marginal revenue curves. At what
quantities do the demand and marginal revenue
lines hit the quantity axis?
- the inverse demand curve is linear, marginal revenue has the same intercept and twice the slope. Thus, if inverse demand is
- P = 300 – 3Q, then marginal
- revenue is
- MR = 300 – 6Q.
- The demand curve
- intersects the horizontal, quantity axis when price equals zero:
p = 300 – 3Q
0 = 300 – 3Q
300 = 3Q
Q = 100 units.
Using a graph, show under what condition the
monopoly operates-does not shut down- in the
long run. Discuss your result in terms of the demand
curve and the average cost curve at the profit-
- A monopoly maximizes profit by producing the quantity where marginal cost (MC) equals marginal revenue (MR). Price is then set according to the demand curve (D).
- The profit-maximizing price and quantity for a monopoly are indicated by point “e” below. The long-run average cost of production at that quantity is indicated by the long-run average cost curve.
- A monopoly will shut down in the long run if it would incur
- losses when producing optimally. A firm will incur losses if its price is less than the long-run average cost of production. Since a monopoly maximizes profit by charging the price indicated by its demand curve at the quantity where marginal revenue equals marginal cost, a monopoly would incur losses when
- producing optimally if the long-run average cost curve is above (greater than) the demand curve at the profit-maximizing quantity.
- For example, at the long-run average cost indicated by LRAC in the graph below, the monopoly breaks even in the long run when producing optimally (at Q*). If long-run average costs were higher, then the monopoly would
- shut down; if lower, it would earn profit.
A monopoly has a constant marginal cost of production of $1 per unit and a fixed cost of $10. Draw the firm's MC, AVC and AC curves. Add a downward sloping demand curve and show the profit maximizing quantity and price. Indicate the profit as an area on your diagram. Show deadweight loss.
- See the figure below. The values of price and quantity depend on the demand curve drawn by the student. Profits are area abcd and the deadweight loss is area bef.
Can a firm operating in the upward-sloping portion
of its average cost curve be a natural monopoly?
Explain. (Hint: See Q&A 9.4.)
- No. In order for a firm to be a natural monopoly, its production must exhibit economies of scale; that is, firm’s average cost curve must be downward sloping. If the firm operates in the upward-sloping region of its average cost curve, it is possible that two or more firms could produce in the same industry
- more efficiently than one firm.
A monopoly currently sells its product at a single
price. What conditions must be met so that it can
profitably price discriminate?
- In order to price discriminate, Alexx must have market power—the ability to set prices. Consumers must have varying price sensitivities, and Alexx must be able to identify individual consumers or groups of individuals based on willingness
- to pay. Alexx must also be able to prevent reselling after the initial sale.
Using a graph, explain why a firm might not want
to spend money on advertising, even if such an
expenditure would shift the firm's demand curve
to the right.
In the figure, let D1 and MR1 be demand and marginal revenue before advertising. Assume the monopoly has a constant marginal cost with no fixed cost such that MC1 = AC1. Then, suppose the monopoly advertises and that the advertising shifts demand and marginal revenue to D2 and MR2.
- Assume advertising is a marginal cost, such that marginal cost
- continues to equal average cost after advertising, and that marginal costs
- remain constant.
- A monopoly maximizes profit by producing the quantity where
- marginal revenue equals marginal cost. For the monopoly to break even from advertising, the marginal cost curve with advertising must shift up by enough that the increase in cost cancels the increase in revenue.
- A marginal cost curve (MC2 = AC2), reflecting the cost of the advertising, is illustrated such that the monopoly breaks even from advertising.
A firm is a natural monopoly (Chapter 9). Its mar-
ginal cost curve is flat, and its average cost curve is
downward sloping (because it has a fixed cost). The
firm can perfectly price discriminate.
a. In a graph, show how much the monopoly produces Q*
b. Can it profitably produce where its price equals its marginal costs?
c. Show that a monopoly might shut down if it can only set a single price but will operate if it can perfectly price discriminate
The monopoly, when maximizing profit at a single price, produces Q* units (where marginal cost equals marginal revenue) and charges the price indicated by the demand curve at the profit-maximizing quantity (p*).
The monopoly could not profitably produce where price equals marginal cost because at that quantity (indicated below by QMC) the price is below the average cost of production, so the monopoly would incur losses.
A patent gave Sony a legal monopoly to produce
a robot dog called Aibo ("eye-BO"). The
Chihuahua-size pooch robot can sit, beg, chase
balls, dance, and play an electronic tune. When
Sony started selling the toy, it announced that it
would sell 3,000 Aibo robots in Japan for about
$2,000 each and a limited litter of 2,000 in the United
States for $2,500 each. Suppose that Sony's marginal
cost of producing Aibo robots was $500. Its inverse
demand functionwasp1==3,500 - ~Q1inJapan and
PA = 4,500 - QA in the United States. Solve for the
equilibrium prices and quantities (assuming that
U.S. customers cannot buy robots from Japan). Show
how the profit-maximizing price ratio depends on
the elasticities of demand in the two countries. What
were the deadweight losses in each country, and in
which was the loss from monopoly pricing greater?
The two marginal revenue curves are MRJ = 3,500 - QJ and MRA = 4,500 - 2QA.
Equating the marginal revenues with the marginal cost of $500, we find that QJ = 3,000 and QA = 2,000. Substituting these quantities into the inverse demand curves, we learn that pJ = $2,000 and pA = $2,500.
We know that the elasticities of demand are eJ = p/(MC - p) = 2,000/(500 - 2,000) = and eA = 2,500/(500 - 2,500) = Thus, we find that
(P1/PA) = 2,000/2,500 = .8 = (1+[1/-5/4]) = (1+[1/Ea])/(1+[1/E1])
The profit in Japan is (pJ- m)QJ = ($2,000 - $500) x 3,000 = $4.5 million, and the U.S. profit is $4 million. The deadweight loss is greater in Japan, $2.25 million (= (1/2) * $1,500 * 3,000), than in the United States, $2 million (= (1/2)* $2,000 ´ *2,000).
A monopoly has a marginal cost of zero and faces
two groups of consumers. At first, the monopoly
could not prevent resale, so it maximized its profit
by charging everyone the same price, p == $5. No
one from the first group chose to purchase. Now
the monopoly can prevent resale, so it decides to
price discriminate. Will total output expand? Why
or why not? What happens to profit and consumer surplus?
Output expands, as do profit and consumer surplus. When the markets are combined, the monopolist sells for $5, all to customers in Market 2. When the markets can be separated, price and quantity remain unchanged in Market 2, but the monopolist also sells for p1.
Joe has just moved to a small town with only one
golf course, the Northlands Golf Club. His inverse
demand function is p = 120 - 2q, where q is the
number of rounds of golf that he plays per year.
The manager of the Northlands Club negotiates
separately with each person who joins the club and
can therefore charge individual prices.This manager
has a good idea of what Joe's demand curve is and
offers Joe a special deal, where Joe pays an annual
membership fee and can play as many rounds as
he wants at $20, which is the marginal cost his
round imposes on the Club. What membership fee
would maximize profit for the Club? The manager
could have charged Joe a single price per round.
How much extra profit does the club earn by using
- A two-part price is where a firm charges a consumer a lump-sum fee for the right to buy as many units of the good as the consumer wants at a specified price. The optimal two-part price for the Club is to charge Joe a per-unit price equal
- to marginal cost ($20) and then set the lump-sum fee equal to Joe’s consumer surplus. Joe’s consumer surplus (CS)
- is equal to the area under his linear demand curve and above the per-round price. This is the area of a triangle with a base equal to the quantity demanded, which is 50 units and a height equal to the difference in where the demand curve hits the vertical, price axis and the $20 price, which is 100:
CS = 0.5(50)(100) = 2,500
- If the firm charges a single price, then the firm maximizes
- profit by setting marginal cost ($20) equal to marginal revenue. The marginal revenue curve is the same as the demand curve but with twice the slope:
MR = 120-4
Setting marginal cost equal to marginal revenue, the profit-maximizing quantity is
The profit-maximizing price is that where consumers demand this quantity:
Profit equals the difference in price ($70) and the marginal cost ($20) multiplied by the units.... Pie = 1,250
- Thus, the difference in profit from using the two-part tariff
- is $1,250 (from profit of $2,500 with the two-part tariff minus profit of $1,250 from charging a single price).
CHAPTER 10 6.2
A computer hardware firm sells both laptop
computers and printers. It has a large inventory of
laptops and printers that it wants to sell, so it has
no variable production cost. Through the magic
of focus groups, their pricing team determines
that they have an equal number of three types of
customers, and that these customers' reservation