Questions and Problems in MANAGERIAL economics
(Choose Any Ten Questions)
(Refer to e-books inside induction2016 folder for answers)
(submit by December 20, by 7.30Pm by email to: bagd@nitrkl.ac.in)
ROLL NO.
1. The economist Arthur Laffer has long argued that lower tax rates, by stimulating employment
and investment, can lead to increased tax revenue to the government. If this prediction is correct, a
tax rate reduction would be a win-win policy, good for both taxpayers and the government. Hint:
X-axis is tax rate (%) & y-axis is unemployment rate(%)
Laffer's tax revenue curve is in the shape of an upside-down U. Explain why the tax base is likely
to shrink as tax rates become very high. How might this lead to a U-shaped tax revenue curve?
2. A firm’s total profit is given by pi =20x + x^2+16y+2y^2.
a. What values of x and y will maximize the firm’s profit (pi)?
b. Repeat part (a) assuming the firm faces the constraint x + y = 8.
c. Repeat part (a) assuming the constraint is x + .5y = 7.5.
3. The price elasticity of demand measures the percentage change in sales for a given percentage
change in the good’s price, all other factors held constant: EP =(Q/Q)/(P/P). Demand is unitary
elastic if EP = 1. In turn, demand is elastic if EP >1. Finally, demand is inelastic if <1 . Revenue is
maximized at the price and quantity for which marginal revenue is zero or, equivalently, the price
elasticity of demand is unity.
In which case of EP, the price responds highest to the sales?
4. The markup price which is linked to a fixed price (plus margin) the rule is (P=MC)/P=1/EP. The
firm’s markup (above marginal cost and expressed as a percentage of price) varies inversely with
the price elasticity of demand for the good or service. (Remember that the firm’s price cannot be
profit maximizing if demand is inelastic.)
What is the maximum margin rate the firm can charge on its goods?
5. During a five-year period, the ticket sales of a city’s professional football team have increased
30 percent at the same time that average ticket prices have risen by 50 percent. Looking at the
change between the two can you imagine an upward-sloping demand curve? Explain.
6. As economic consultant to a big firm in a particular market, you have discovered that, at the
current price and output, demand for your client’s product is price inelastic (EP=0). What advice
regarding pricing would you give?
7. A baseball team is trying to predict ticket sales for the upcoming season and is considering
changing ticket prices.
a. The elasticity of ticket sales with respect to the size of the local population is estimated to be
about (EP) = .7. Briefly explain what this number means. If the local population increases from
60,000 to 61,500, what is the predicted change in ticket sales?
b. Currently, a baseball fan pays an average ticket price of $10. The price elasticity of demand for
tickets is EP= -0.6. Management is thinking of raising the average ticket price to $11. Compute the
predicted change in ticket sales?
8. a. General Motors (GM) produces light trucks in several Michigan factories, where its annual
fixed costs are (F) $180 million, and its marginal cost (MC) per truck is approximately $20,000.
Regional demand for the trucks is given by:
P = 30,000 -0.1Q,
where P denotes price in dollars and Q denotes annual sales of trucks. Find GM’s profit
maximizing output level and price. Find the annual profit generated by light trucks.
b. GM is getting ready to export trucks to several markets in South America. Based on several
marketing surveys, GM has found the elasticity of demand in these foreign markets to be EP= 9 for
a wide range of prices (between $20,000 and $30,000). The additional cost of shipping (including
paying some import fees) is about $800 per truck.
One manager argues that the foreign price should be set at $800 above the domestic price (in part
a) to cover the transportation cost. Do you agree that this is the optimal price for foreign sales?
Justify your answer.
9. During the 1990s, Apple Computer saw its global share of the personal computer market fall
from above 10 percent to less than 5 percent. Despite a keenly loyal customer base, Apple found it
more and more difficult to compete in a market dominated by the majority standard: PCs with
Microsoft’s Windows-based operating system and Intel’s microchips. Indeed, software developers
put a lower priority on writing Mac applications than on Windows applications. Demand is given
as, P =30,000-Q.
a. In the early 1990s, Apple enjoyed high markups on its units. In 1995 Apple’s chief, John
Sculley, insisted on keeping Mac’s gross profit margin at 50 to 55 percent, even in the face of
falling demand. (Gross profit margin is measured as total revenue minus total variable costs
expressed as a percentage of total revenue.) At this time, the business of selling PCs was becoming
more and more “commodity-like.” Indeed, the price elasticity facing a particular company was
estimated in the neighborhood of EP=4.
b. Apple has discontinued several of its lower-priced models and has expanded its efforts in the
education and desktop publishing markets. In addition, recent software innovations allow Macs to
read most documents, data, and spreadsheets generated on other PCs. Do these initiatives make
sense? How will they affect demand?
10. a. Triple cast was NBC’s and Cablevision’s joint venture to provide payper-view cable
coverage of the 1992 Summer Olympics in Barcelona. Based on extensive surveys of potential
demand, the partners hoped to raise $250 million in revenue by attracting some 2 million
subscribers for three channels of nonstop Olympics coverage over 15 days. NBC set the average
package price at $125 for complete coverage and offered a separate price of $29.95 per day.
However, as the games began, fewer than 400,000 homes had subscribed.
After experiencing the unexpectedly lukewarm response prior to the games, what strategy would
you recommend that NBC pursue?
11. In 1997, America Online (AOL) overhauled its pricing of Internet access. Formerly,
subscribers paid a monthly fee of $9.95 (good for a limited number of access hours) and paid an
additional fee for each hour exceeding the limit. In a bid to increase its customer base, AOL
offered a new plan allowing unlimited access at a fixed monthly fee of $19.95. (The company
estimated that the new plan would deliver a cheaper effective rate per hour for the vast majority of
its current customers.)
i. what are the pros and cons of AOL’s unlimited access pricing plan?
ii. What is the net impact on costs ?
12. A New Hampshire resort offers year-round activities: in winter, skiing and other cold-weather
activities and, in summer, golf, tennis, and hiking. The resort’s operating costs are essentially the
same in winter and summer. Management charges higher nightly rates in the winter, when its
average occupancy rate is 75 percent, than in the summer, when its occupancy rate is 85 percent.
Can this policy be consistent with profit maximization? Explain.
13. In 1996, the drug Prilosec became the best-selling anti-ulcer drug in the world. (The drug was
the most effective available, and its sales outdistanced those of its nearest competitor.) Although
Prilosec’s marginal cost (production and packaging) was only about $.60 per daily dose, the drug’s
manufacturer initially set the price at $3.00 per dose—a 400 percent markup relative to MC? Will
you call Prilosec a monopolist, Duopolist, leader? What?
14. In what respects are the following common practices subtle (or not-so subtle) forms of price
discrimination?
a. Frequent-flier and frequent-stay programs
b. Manufacturers’ discount coupon programs
c. A retailer’s guarantee to match a lower competing price
15. A private-garage owner has identified two distinct market segments: short-term parkers and
all-day parkers with respective demand curves of PS (short) =3 + (QS/200) and PC(full day) =2 +
(QC/200).
Here P is the average hourly rate and Q is the number of cars parked at this price.
The garage owner is considering charging different prices (on a per-hour basis) for short-term
parking and all-day parking. The capacity of the garage is 600 cars, and the cost associated with
adding extra cars in the garage (up to this limit) is negligible.
a. Given these facts, what is the owner’s appropriate objective? How can he ensure that members
of each market segment effectively pay a different hourly price?
b. What price should he charge for each type of parker? How many of each type of parker will use
the garage at these prices? Will the garage be full? c. Answer the questions in part (b) assuming the
garage capacity is
400 cars.
16. Because of changing demographics, a small, private liberal arts college predicts a fall in
enrollments over the next five years. How would it apply marginal analysis to plan for the
decreased enrollment?
17. Suppose a firm’s inverse demand curve is given by P=120 +.5Q and its cost equation is C =420
+ 60Q + Q^2.
a. Find the firm’s optimal quantity, price, and profit (1) by using the profit and marginal profit
equations and (2) by setting MR equal to MC. Also provide a graph of MR and MC.
b. Suppose instead that the firm can sell any and all of its output at the fixed market price P =120.
Find the firm’s optimal output.
18. a. the demand continues to be given by P -120, but the firm’s cost equation is linear: C=420 +
60Q. . At what quantity does the firm break even, that is, earn exactly a zero profit?
b. In general, suppose the firm faces the fixed price P and has cost equation C = F + cQ, where F
denotes the firm’s fixed cost and c is its marginal cost per unit. Write down a formula for the firm’s
profit. Set this expression equal to zero and solve for the firm’s break-even quantity (in terms of P,
F, and c).
c. In this case, what difficulty arises in trying to apply the MR=MC rule to maximize profit? By
applying the logic of marginal analysis, state the modified rule applicable to this case.
19. A television station is considering the sale of promotional videos. It can have the videos
produced by one of two suppliers. Supplier A will charge the station a set-up fee of $1,200 plus $2
for each DVD; supplier B has no set-up fee and will charge $4 per DVD. The station estimates its
demand for the DVDs to be given by Q =1,600 - 200P, where P is the price in dollars and Q is the
number of DVDs. (The price equation is P=8 + Q/200.)
a. Suppose the station plans to give away the videos. How many DVDs should it order? From
which supplier?
b. Suppose instead that the station seeks to maximize its profit from sales of the DVDs. What price
should it charge? How many DVDs should it order from which supplier? (Hint: Solve two separate
problems, one with supplier A and one with supplier B, and then compare profits. In each case,
apply the MR = MC rule.)
20. The college and graduate-school textbook market is one of the most profitable segments for
book publishers. A best-selling accounting text published by Old School Inc (OS)—has a
demand curve: P =150 -Q,
where Q denotes yearly sales (in thousands) of books. (In other words, Q =20 means 20 thousand
books.) The cost of producing, handling, and shipping each additional book is about $40, and the
publisher pays a $10 per book royalty to the author. Finally, the publisher’s overall marketing and
promotion spending (set annually) accounts for an average cost of about $10 per book.
a. Determine OS’s profit-maximizing output and price for the accounting text.
b. A rival publisher has raised the price of its best-selling accounting text by $15. One option is to
exactly match this price hike and so exactly preserve your level of sales. Do you endorse this price
increase? Explain briefly why or why not.
c. To save significantly on fixed costs, Old School plans to contract out the actual printing of its
textbooks to outside vendors. OS expects to pay a somewhat higher printing cost per book (than in
part a) from the outside vendor (who marks up price above its cost to make a profit). How would
outsourcing affect the output and pricing decisions in part (a)?
21. As the exclusive carrier on a local air route, a regional airline must determine the number of
flights it will provide per week and the fare it will charge. Taking into account operating and fuel
costs, airport charges, and so on, the estimated cost per flight is $2,000. It expects to fly full flights
(100 passengers), so its marginal cost on a per passenger basis is $20. Finally, the airline’s
estimated demand curve is P=120 + .1Q, where P is the fare in dollars and Q is the number of
passengers per week.
a. What is the airline’s profit-maximizing fare? How many passengers does it carry per week,
using how many flights? What is its weekly profit?
b. Suppose the airline is offered $4,000 per week to haul freight along the route for a local firm.
This will mean replacing one of the weekly passenger flights with a freight flight (at the same
operating cost). Should the airline carry freight for the local firm? Explain.
22. A producer of photocopiers derives profits from two sources: the immediate profit it makes on
each copier sold and the additional profit it gains from servicing its copiers and selling toner and
other supplies.
R= 720 + 8t and C =600 +20t + .25t^2,
The firm estimates that its additional profit from service and supplies is about $300 over the life of
each copier sold.
There is disagreement in management about the implication of this tie-in profit. One group argues
that this extra profit (though significant for the firm’s bottom line) should have no effect on the
firm’s optimal output and price. A second group argues that the firm should maximize its total
profit by lowering price to sell additional units (even though this reduces its profit margin at the
point of sale). Which view is correct?
23. Suppose the microchip producer discussed in this chapter faces demand and cost equations
given by Q= 8.5 = .05P and C=100. Modifying a product to increase its “value added” benefits
customers and can also enhance supplier profits. For example, suppose an improved version of a
product increases customer value added by $25 per unit. (In effect, the demand curve undergoes a
parallel upward shift of $25.)
a. If the redesign is expected to increase the item’s marginal cost by $30, should the company
undertake it?
b. Suppose instead that the redesign increases marginal cost by $15. Should the firm undertake it at
what output and price?
24. Suppose a firm’s inverse demand and cost equations are of the general forms P = a + bQ and C
=F +cQ, where the parameters a and b denote the intercept and slope of the inverse demand
function and the parameters F and c are the firm’s fixed and marginal costs, respectively. Apply
the MR =MC rule to confirm that the firm’s optimal output and price are: Q = (a + c)/2b and P = (a
+c)/2. Provide explanations for the ways P and Q depend on the underlying economic parameters.
25. Under the terms of the current contractual agreement, Burger Queen (BQ) is entitled to 20
percent of the revenue earned by each of its franchisee sales. BQ’s best-selling item is the Slopper
(it slops out of the bun). BQ supplies the ingredients for the Slopper (bun, mystery meat, etc.) at
cost to the franchise. The franchisee’s average cost per Slopper (including ingredients, labor cost,
and so on) is $.80. At a particular franchise restaurant, weekly demand for Sloppers is given by P
=3.00 - Q/800.
a. If BQ sets the price and weekly sales quantity of Sloppers, what quantity and price would it set?
b. Suppose the franchise owner sets the price and sales quantity. What price and quantity will the
owner set? (Hint: Remember that the owner keeps only $.80 of each extra dollar of revenue
earned.)
26. Suppose a firm assesses its profit function(pi) as pi= 2.5+0.5Q+0.25Q^2
a. Compute the firm’s profit for the following levels of output: Q = 2, 8,and 14.
b. Derive an expression for marginal profit. Compute marginal profit at Q = 2, 8, and 14. Confirm
that profit is maximized at Q = 8. (Why is profit not maximized at Q =2?)
27. A golf-course operator must decide what greens fees (prices) to set on rounds of golf. Daily
demand during the week is: PD =36-QD/10, where QD is the number of 18-hole rounds and PD is
the price per round.
Daily demand on the weekend is: PW =50 - QW/12. As a practical matter, the capacity of the
course is 240 rounds per day. Wear and tear on the golf course is negligible.
Can the operator profit by charging different prices during the week and on the weekend? Explain
briefly. What greens fees should the operator set on weekdays, and how many rounds will be
played? On the weekend?
28. Let’s consider the maker of spare parts to determine its optimal price. The firm’s demand curve
is given by
Q = 400 - 0.5P and its cost function by C =20,000 +200Q -.5Q2.
a. Treating price as the relevant decision variable, compute the price elasticity o EP =
(dQ/dP)(P/Q).
b. Find the optimal price by hand. (Hint: Vary price while comparing . When (PMC)/P exactly
equals=1/EP, the
markup rule is satisfied and the optimal price has been identified.) Elasticity MC (P=MC)/P =1/EP
29. On a popular air route, an airline offers two classes of service: business class (B) and economy
class (E). The respective demands are given by:
Because of ticketing restrictions, business travelers cannot take advantage of economy’s low fares.
The airline operates two flights daily. Each flight has a capacity of 200 passengers. The cost per
flight is $20,000.
a. The airline seeks to maximize the total revenue it obtains from the two flights.
b. What fares should the airline charge, and how many passengers will buy tickets of each type?
Remember that maximum revenue is obtained by setting MRB equal to MRE. After you have
explored the decision by hand, (Hint: Be sure to include the constraint that the total PB = 540
-.5QB and PE =380 - .25QE.
number of seats sold must be no greater than the total number of seats available
c. Suppose the airline is considering promoting a single “value fare” to all passengers along the
route. Find the optimal single fare (Hint: Simply modify the optimizer instructions from part (b) by
adding the constraint that the prices must be equal.)
30. Indifference curves- a price-consumption curve that passes through the optimal consumption
points. This curve shows the consumer’s optimal consumption as the price of X is varied
continuously. Using this curve, we can record the consumption of X at each price. If we plot the
quantity of X demanded versus its price, we arrive at the consumer’s demand curve for X; it has
the usual downward slope. The consumer increases her optimal consumption of X in response to
lower prices. Of course, different individuals will have varying preferences for goods and varying
incomes. For these reasons, they obviously will have different
demand curves. How do we arrive at the market demand curve (the total demand by all consumers
as price varies)? The answer is found by summing the quantities demanded by all consumers at any
given price.
a. Consider a different consumer who has much steeper indifference curves. What do these curves
imply about his relative valuation for good X versus good Y?
b. Using the curves from part (a) and the budget line Equation graph the consumer’s optimal
consumption bundle. How does his consumption bundle compare with that of the original
consumer?
31. a. Suppose the income the consumer has available to spend on goods increases to $30. Graph
the new budget line and sketch a new indifference curve to pinpoint the consumer’s new optimal
consumption bundle. According to your graph, does the consumer purchase more of each good?
b. Imagine a graph (with an appropriate indifference curve) in which one of the goods is inferior.
That is, the rise in income causes the consumer to purchase less of one of the goods.
32. Suppose that the price of good X rises and the price of good Y falls in such a way that the
consumer’s new optimal consumption bundle lies on the same indifference curve as his old bundle.
Imagine the Graph this situation. Compare the quantities demanded between the old and new
bundles.
33. A study of cigarette demand resulted in the following logarithmic regression equation:
log(Q) = -2.55-0.29log(P)-.09log(Y) + .08log(A)
Here, Q denotes annual cigarette consumption, P is the average price of cigarettes, Y is per capita
income, and A is total spending on cigarette advertising.
a. Which of the explanatory variables have real effects on cigarette consumption? Explain.
b. What does the coefficient of log(P) represent? If cigarette prices increase by 20 percent, how
will this affect consumption?
c. Are cigarette purchases sensitive to income? Explain.
34. The following regression was estimated for 23 quarters between 2004 and 2011 to test the
hypothesis that tire sales (T) depend on new automobile sales (A) and total miles driven (M).
a. Does the regression equation (and its estimated coefficients) make economic sense? Explain.
b. Based on the regression output, discuss the statistical validity of the equation.
c. Do the coefficients on “miles driven” and “new-auto sales” significantly differ from 1.0?
Explain why we might use unity as a benchmark for these coefficients.
d. Suppose that we expect “miles driven” to fall by 2 percent and “new auto sales” by 13 percent
(due to a predicted recession). What is the predicted change in the sales quantity of tires? If actual
tire sales dropped by 18 percent, would this be surprising?
a. A fellow manager points to the 15-unit increase between year 3 and year 4. Extrapolating this
trend, he predicts 135 units will be sold in the coming year (year 5). Do you agree? Explain.
b. Does optimal use of an input (such as labor) mean maximizing average output (per unit of
input)? Explain.
36. Consider the production function Q = 10L + .5L2 + 24K + K2 for L and K in the range 0 to 10
units. Does this production function exhibit diminishing returns to each input? Does it exhibit
decreasing returns to scale? Explain. Suppose input prices are PL= 40 and PK =80 and the price of
output is 10. Determine the optimal quantity of each input.
37. Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking
firm is well described by the equation Q= L + L2/800, where Q denotes the number of dresses per
week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra
hour of labor is about $20 per hour (wage plus fringe benefits).
The firm faces the fixed selling price, P =$40.
a. How much labor should the firm employ? What is its resulting output and profit?
b. Over the next two years, labor costs are expected to be unchanged, but dress prices are expected
to increase to $50. What effect will this have on the firm’s optimal output? Explain. Suppose
instead that inflation is expected to increase the firm’s labor cost and output price by identical
(percentage) amounts. What effect would this have on
the firm’s output?
c. Finally, suppose once again that MCL = $20 and P = $50 but that labor productivity (i.e., output
per labor hour) is expected to increase by 25 percent over the next five years. What effect would
this have on the firm’s optimal output? Explain.
27. The rancher’s cost of grass is $.10 per pound; the cost of grain is $.07 per pound. He prefers a
feed mix of 68 pounds of grass and 60 pounds of grain. Is this a least-cost mix? If not, what is?
Explain.
c. The rancher believes there are constant returns to scale in fattening cattle. At current feed prices,
what input quantities should he choose if he wants to raise the steer’s weight to 250 pounds?
38. A trendy French restaurant is one of the first businesses to open in a small corner of a
commercial building still under construction. The restaurant has received rave reviews and has
lines of diners waiting for tables most nights.
a. In the short run (next few months), what measures should the restaurant take to maximize its
profit? Explain.
b. In the long run (next six months and beyond), how can it maximize its profit? (Assume that the
impressive state of demand is permanent.)
39. In recent years, Chrysler Corporation initiated three-shift or nearly continuous
(21-hours-per-day) production at a number of its plants. Explain why Chrysler’s decision might
have been prompted by movements in its wage costs or capital costs, or both. Why would Chrysler
have instituted this production change for its most popular (and profitable) vehicles, its minivans
and Jeep Cherokee? What risks might such a plan pose?
40. A firm is producing a given amount of output at least cost using a mix of labor and capital
(which exhibit some degree of substitutability). Using an isoquant graph, show that if one input
price increases, least-cost production calls for the firm to reduce that input (and increase the use of
the other).
41. Consider the production function Q =100L.5K.4. Suppose L = 1 and K =1 so that Q =100.
a. If L is increased by 1 percent, that is, to L =1.01, with capital unchanged, what is the resulting
percentage increase in output?
b. Describe the nature of returns to scale for this production function.
42. In a particular region, there are two lakes rich in fish. The quantity of fish caught in each lake
depends on the number of persons who fish in each, according to Q1= 10N1 _.1N1 2 and Q2 =
16N2 + .4N2 2, where N1 and N2
denote the number of fishers at each lake. In all, there are 40 fishers.
a. Suppose N1 =16 and N2 = 24. At which lake is the average catch per fisher greater? In light of
this fact, how would you expect the fishers to re-deploy themselves?
b. How many fishers will settle at each lake? (Hint: Find N1 and N2 such that the average catch is
equal between the lakes.)
c. The commissioner of fisheries seeks a division of fishers that will maximize the total catch at the
two lakes. Explain how he should use information on the marginal catch at each lake to accomplish
this goal. What division of the 40 fishers would you recommend?
43. A firm’s production function is well described by the equation Input prices are $10 per labor
hour and $20 per machine hour, and the firm sells its output at a fixed price of $10 per unit.
Q =2L + 01L2 x 3K + .02K2.
a. In the short run, the firm has an installed capacity of machine hours per day, and this capacity
cannot be varied. Determine the firm’s profit-maximizing employment of labor. Confirm that
MRPL =MCL. K = 50
b. Suppose the firm were to downsize in the long run, cutting its use of both inputs by 50 percent
(relative to part b). How much output would it now be able to produce? Comment on the nature of
returns to scale in production. Has the firm’s profitability improved? Is it currently achieving
least-cost production?
44. A second firm’s production function is given by the equation Input prices are $36 per labor unit
and $16 per capital unit, and P = $10.
a. In the short run, the firm has a fixed amount of capital, K =9. Determine the firm’s
profit-maximizing employment of labor.
b. Once again, the firm seeks to produce the level of output found in part (a) by adjusting both
labor and capital in the long run. Find the least-cost input proportions. Confirm that MPL/PL
=MPK/PK. Q =12L.5K.5
c. Suppose the input price of labor falls to $18. Determine the new least cost input amounts in the
long run. Provide an intuitive explanation for the change in inputs caused by the lower labor price.
45. The development of a new product was much lengthier and more expensive than the
company’s management anticipated. Consequently, the firm’s top accountants and financial
managers argue that the firm should raise the price of the product 10 percent above its original
target to help recoup some of these costs. Does such a strategy make sense?
Explain carefully.
46. A company produces two main products: electronic control devices and specialty microchips.
The average total cost of producing a microchip is $300; the firm then sells the chips to other
high-tech manufacturers for $550. Currently, there are enough orders for microchips to keep its
factory capacity fully utilized. The company also uses its own chips in the production of control
devices. The average total cost (AC) of producing such a device is $500 plus the cost of two
microchips. (Assume all of the $500 cost is variable and AC is constant at different output
volumes.) Each control device sells for an average price of $1,500.
a. Should the company produce control devices? Is this product profitable?
b. Answer part (a) assuming outside orders for microchips are insufficient to keep the firm’s
production capacity fully utilized.
c. Now suppose $200 of the average cost of control devices is fixed. Assume, as in part (a), that
microchip capacity is fully utilized. Should control devices be produced in the short run? Explain.
6. Suppose the manufacturer of running shoes has collected the following quantitative
information. Demand for the boys’ shoe is estimated to be Q = 9,600 -200P, or, equivalently, P =
48 - Q/200. The shoe’s direct cost is C = $60,000 + .0025Q2.
Find the firm’s profit-maximizing price and output.
47. Firm A makes and sells motorcycles. The total cost of each cycle is the sum of the costs of
frames, assembly, and engine. The firm produces its own engines according to the cost equation:
The cost of frames and assembly is $2,000 per cycle. Monthly demand for cycles is given by the
inverse demand equation P =10,000 -30Q.
a. What is the MC of producing an additional engine? What is the MC of producing an additional
cycle? Find the firm’s profit-maximizing quantity and price. CE =250,000 + 1,000Q+ 5Q2.
b. Now suppose the firm has the chance to buy an unlimited number of engines from another
company at a price of $1,400 per engine. Will this option affect the number of cycles it plans to
produce? Its price?
Will the firm continue to produce engines itself? If so, how many?
948 A firm’s long-run total cost function is
a. What is the shape of the long-run average cost curve?
b. Find the output that minimizes average cost.
c. The firm faces the fixed market price of $140 per unit. At this price, can the firm survive in the
long run? Explain.
49. A firm uses a single plant with costs C = 160 + 16Q =+ .1Q2 and faces the
price equation P = 96 -.4Q.
a. Find the firm’s profit-maximizing price and quantity. What is its profit?
b. The firm’s production manager claims that the firm’s average cost of production is minimized at
an output of 40 units. Furthermore, she claims that 40 units is the firm’s profit-maximizing level of
output. Explain whether these claims are correct.
c. Could the firm increase its profit by using a second plant (with costs identical to the first) to
produce the output in part (a)? Explain.
50.General Motors (GM) produces light trucks in its Michigan factories. Currently, its Michigan
production is 50,000 trucks per month, and its marginal cost is $20,000 per truck. With regional
demand given by: P = 30,000 - 0.1Q, GM sets a price of $25,000 per truck.
a. Confirm that setting Q = 50,000 and P = $25,000 is profit maximizing.
b. General Motors produces the engines that power its light trucks and finds that it has some
unused production capacity, enough capacity to build an additional 10,000 engines per year. A
manufacturer of sports utility vehicles (SUVs) has offered to purchase as many as 25,000 engines
from GM at a price of $10,000 per engine. GM’s contribution is estimated to be about $2,000 per
engine sold (based on a marginal cost of $8,000 per engine). Should GM devote some of its engine
capacity to produce engines to sell to the SUV manufacturer? Does this outside opportunity
change GM’s optimal output of light vehicles in part (a)?
c. GM also assembles light trucks in a West Coast facility, which is currently manufacturing
40,000 units per month. Because it produces multiple vehicle types at this mega-plant, the firm’s
standard practice is to allocate $160 million of factory wide fixed costs to light trucks. Based on
this allocation, the California production manager reports
that the average total cost per light truck is $22,000 per unit. Given this report, what conclusion (if
any) can you draw concerning the C = 360 + 40Q =+10Q2.
marginal cost per truck? If West Coast demand is similar to demand in Michigan, could the West
Coast factory profit by changing its output from 40,000 units?
51. A manufacturing firm produces output using a single plant. The relevant cost function is C _
500 _ 5Q2. The firm’s demand curve is P = 600 - 5Q.
a. Find the level of output at which average cost is minimized. Hint: Set AC equal to MC. What is
the minimum level of average cost?
b. Find the firm’s profit-maximizing output and price. Find its profit.
c. Suppose the firm has in place a second plant identical to the first. Argue that the firm should
divide production equally between the plants.
Check that the firm maximizes profit at total output Q* such that MR(Q*) = MC1(Q*/2) +
MC2(Q*/2).
C = 175,000 + 300Q + .1Q2.
P =800 - .15Q,
Explain why total output is greater than in part (b).
d. In the long run, the firm can produce using as many or as few plants as it wishes (each with the
preceding cost function). In this case, what kind of returns to scale hold? What are the firm’s
optimal output and price in the long run? How many plants will the firm use to produce the good?
Hint: Refer to the value of minimum AC you found in part (a).
52. A firm produces digital watches on a single production line serviced during one daily shift. The
total output of watches depends directly on the number of labor-hours employed on the line.
Maximum capacity of the line is 120,000 watches per month; this output requires 60,000 hours of
labor per month. Total fixed costs come to $600,000 per month, the wage rate averages $8 per
hour, and other variable costs (e.g., materials) average $6 per watch. The marketing department’s
estimate of demand is P = 28 - Q/20,000, where P denotes price in dollars and Q is monthly
demand.
a. How many additional watches can be produced by an extra hour of labor? What is the marginal
cost of an additional watch? As a profit maximizer, what price and output should the firm set? Is
production capacity fully utilized? What contribution does this product line provide?
b. The firm can increase capacity up to 100 percent by scheduling a night shift. The wage rate at
night averages $12 per hour. Answer the questions in part (a) in light of this additional option.
c. Suppose that demand for the firm’s watches falls permanently to P =20 - Q/20,000. In view of
this fall in demand, what output should the firm produce in the short run? In the long run? Explain.
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