University of Toronto
Department of Economics
ECO101: Principles of Microeconomics
Robert Gazzale, PhD
Term Test 2 2018: Gazzale Regular
Solutions: Full
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20181119GazzaleRegular
Term Test 2: Solutions: Full
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General Instructions
105 minutes. 106 marks. Allocate your time wisely!
OTHER test booklet: Multiple choice questions. 53 marks.
THIS test booklet: Short answer and calculation questions. 53 marks.
THIS test booklet: Record multiple-choice answers on last page.
Aids allowed: a non-graphing, non-programmable calculator; a straight edge (i.e., ruler).
For True, False or Uncertain questions, all marks are earned for the explanation.
Show your work. No work, no partial marks.
When explanations are needed, be clear, accurate, and concise.
Avoid the temptation to write too much.
The final page is blank. If you need to continue an answer on this page, you must write
“Continued on final page” in the question’s answer space.
Unless otherwise stated, assume quantities need not be integers.
I. [25 Marks] TFU means “True, False or Uncertain?”. All marks are earned for the explanation.
(1) [5 Marks] You are organizing a charity concert. You must sell each ticket at the same price. You
will donate the difference between total revenues and total costs to the charity. Drake has agreed
to perform, for free! You rented the 19,900-seat Scotiabank Arena, for $1! Given the downwardsloping linear demand curve for tickets, you correctly calculate that $500 per ticket maximizes
the charitable donation. Then, you then learn that that you have to pay a $5 per-attendee
“security charge”. TFU: $500 still maximizes the charitable donation.
Suggested Solution: Uncertain. It is true when you M R = M C at a quantity greater than
19,900. (The is the same as M R > M C at 19,900. If M C = 0, it is the same as demand is elastic
at 19,900). In this case, you find the price where Qd = 19, 900, and your supply is perfectly
inelastic at this price. Because your supply is perfectly inelastic, you bear the full incidence of
the tax.
False when M R = M C at a quantity less than 19,900. You do not plan on selling all the tickets.
In this case, you are selling a quantity were M R = M C. This increase in marginal cost causes
you to reduce quantity and increase price. (With a linear demand curve, the increase in price is
exactly $2.50.)
(2) [5 Marks] Assume a perfectly competitive market where quantities must be integers and supply
and demand schedules are depicted in the following table.
Q
MWTP
MC
1
$21
$5
2
$18
$8
3
$16
$10
4
$14
$12
5
$12
$14
6
$10
$16
7
$8
$18
TFU: If the equilibrium price without government intervention is $13, then a price ceiling at
$11 increases consumer surplus by $5.
Suggested Solution: Uncertain. Originally, four units are transacted, with the four highest
MWTP getting the item. With the ceiling at P = $11, only three units are supplied and thus
only three units are transacted. IF these three items go to the highest MWTP, then the increase
in CS is $5. The three highest pay $2 less, for a total increase of $6, but consumer four no longer
transacts and we thus lose the $1 in surplus she got. HOWEVER, there are five consumers
willing to pay at least $11, and consumer surplus will be reduced if either four or five gets an
item (i.e., if the items do not go to the highest WTP consumers).
20181119GazzaleRegular
Term Test 2: Solutions: Full
(3) [5 Marks] Assume quantities need not be integers. I am offering you the opportunity to be the
only seller of silent velcro in Toronto, where per-period demand is P (Q) = 20 − Q. If you accept,
you pay me a fixed cost of $30 per period and $10 for each unit you sell. These are your only
costs. TFU: You should accept the offer to be the only seller of silent velcro in Toronto.
Suggested Solution: Uncertain. If you are constrained to charging the same price for each
unit, you charge $15, earning $5 on each of 5 units. This is not sufficient to cover your fixed costs.
However, if you can price discriminate, you can increase PS. At best, you engage in first-degree
price-discrimination and earn $50 in PS each period. In this case, you should accept.
Note: For full marks, you need to establish that it is possible for price discrimination to result
in at least $30 in surplus. After all, the statement would be false if the fixed cost was $100.
(4) [5 Marks] You are a monopolist constrained to charging the same price for each unit who faces
a standard linear demand curve. You have correctly calculated that your profit maximizing price
is $10 and you would sell 1000 units at this price. TFU: A price ceiling set at P = $9 reduces
your short-run profits by $1000.
Suggested Solution: False. Your short-run profits (i.e., fixed costs minus producer surplus)
decrease by less than $100. For the 1000 items you would have sold at P = $10, you lose $1 in
surplus on each for a reduction of $1000. However, you will sell more units at P = $9, and you
make some P S on each of these extra units.
Note: You lost marks if you wrote that this could increase profits. As producer surplus, and
thus profits, are maximized at P = $10, profits must be less at any other price.
(5) [5 Marks] Assume labour must be purchased in integer quantities at $20 per unit. You have
incurred a fixed cost equal to $1000, and each item you produce requires $9 in materials and
some labour. Currently, you produce and sell 1002 units at $20 each. TFU: If the marginal
product of the last worker you hired was 2, then hiring this worker increased your profits.
Suggested Solution: Uncertain. By hiring this worker, you increased your costs by $38: $20
in labour and $9 × 2 = $12 in materials.
If you are a firm in a perfectly competitive market, then you can sell as much as you want at the
market price of $20 for a benefit of $40. As the marginal benefit was greater than the marginal
cost, this increased your producer surplus and thus your profit.
However, if your firm has market power, we have to consider the price effect: you would have
gotten a slightly higher price had you not hired the last worker and only sold 1000.
II. [12 Marks] Kipchoge Enterprises (KE) provides coaching services. Eliud is both the owner and
only employee (i.e., coach). Each period, KE pays $1550 in rent, and faces per-period demand
P (Q) = M W T P (Q) = 120 − Q, where Q is the number of hours of coaching Eliud provides. By law,
coaches must be paid exactly $20 per hour. (While KE must pay Eliud $20 per hour, KE can charge
customers whatever it likes.)
(1) [4 Marks] If KE had to charge the same price for each hour of coaching services and KE
maximized accounting profits, what are KE’s accounting profits?
20181119GazzaleRegular
Term Test 2: Solutions: Full
Suggested Solution: The math:
M R(Q∗M ) = M C(Q∗M )
120 −
120 −
2Q∗M
2Q∗M
=
M C(Q∗M )
= $20
100 =
profit maximization
twice-as-steep rule
substituting
2Q∗M
Q∗M = $50
P (Q∗M ) = 120 − Q∗M
∗
PM
∗
πM
solving for price
= 120 − 50 = $70
∗
= P SM
−F
= ($70 − $20) × 50 − $1550
= $2500 − $1550 = $950
Because with have linear demand an constant M C, you could have saved a little math if you
remembered that the profit maximizing price if halfway between the vertical intercept of the
= $70.
demand curve and the marginal cost: P m = 120+20
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(2) [3 Marks] You find out that every hour Eliud worked for his firm, he could have either worked
for Keitany Consulting at $40 per hour or Uber at $15 per hour. Concisely explain to Eliud
(who has never heard of the economics terms you now know) why accounting profits are not the
true measure of KE’s profitability.
Suggested Solution: A general answer: We want to do anything where the benefit is greater
than the cost. The “firm” is choosing the number of hours assuming the cost is $20. The true
cost, however, is $40 per hour, as every hour he works for KE he is giving up $40.
If you went the example way: Eliud keeps every extra dollar generated whether as salary or
profit. As hour of consulting that generates $30 in revenues seems profitable as it is greater than
the $20, but is not profitable because Eliud gave up $40 to generate the $30.
Note: For full marks, you must make it clear that the true cost to Eliud of using his time for
his business is $40.
(3) [5 Marks] KE’s current lease is complete and Eliud now has the choice whether commit to
paying $1550 per-period in rent. Given his costs, the demand for Eliud’s coaching services
(P (Q) = M W T P (Q) = 120 − Q), and the fact that KE must charge the same price for each
hour, should KE sign a new lease? (Full marks are given for the explanation.)
Suggested Solution: If he continues to provide 50 hours per month, his true producer surplus
is ($70 − $40) × 50 = $1500, which means that his business would not be profitable as his fixed
cost is $1550.
However, to find the number of hours maximizing his economic profits, he should use his true
marginal cost of $40 per hour. P m = 120+40
= $80. Qm = 40. P S = ($80 − $40) × 40 = $1600.
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π = 1600 − 1550 = 50. So yes, the business is profitable and he should sign the lease.
III. [16 Marks] Assume continuous quantities. Coffee roasting is perfectly competitive in Boblandia. All
firms face the same costs. To roast coffee, a firm must rent one coffee roasting machine at 50 Bobos
per period, and then incurs a marginal cost for each pound roasted. In particular, to roast qi pounds,
20181119GazzaleRegular
Term Test 2: Solutions: Full
a firm’s costs are:
M C(qi ) = 10 + qi
T C(qi ) = 50 + 10qi +
marginal cost
qi2
2
total cost
(1) [2 Marks] Labelling any and all lines or curves, in the graph below clearly identify PBE , the
price at which a firm earns zero economic profits in the short run. (Hint: You need two “curves”.
The curves need to be qualitatively correct. They do not need to be numerically correct.)
Suggested Solution: Your graph will have a U-shaped AT C, will have the upward-sloping
portion of the M C intersect AT C at AT Cmin , and will show that PBE is the minimum value of
the AT C.
Note: The M C in this question is everywhere upward sloping.
(2) [3 Marks] If the price is PBE , clearly but concisely explain how your graph shows economic
profits are zero.
Suggested Solution: The behavioural rule is to keep increasing output as long as MB (the
market price, in a competitive market) is at least as large as marginal cost. This means finding
the quantity (qi∗ ) where MC=P. At PBE , ATC=P, meaning total revenue (PBE × qi∗ ) equals total
costs (AT C(qi∗ ) × qi∗ ).
Note: For full marks, you must be clear that M C determines your quantity. That is, when
the price is where AT C = M C (i.e., the minimum of the ATC), you stop at the quantity where
P = AT C.
20181119GazzaleRegular
Term Test 2: Solutions: Full
M C(qi ) = 10 + qi
T C(qi ) = 50 + 10qi +
marginal cost
qi2
2
total cost
(3) [4 Marks] Solve for the price at which firms in the market earn zero economic profits.
Suggested Solution: We need to find the minimum of the ATC curve. To find AT C(qi ), take
T C(qi ) and divide by qi . The minimum of the ATC occurs at the qi where AT C = M C.1
AT C(qi ) = M C(qi )
q
50
+ 10 + = 10 + qi
qi
2
50 q
+ = qi
qi
2
50
q
=
qi
2
100 = qi2
at AT Cmin
substituting
qi = 10
To find the value of ATC at AT Cmin , substitute qi = 10 into either MC or ATC. PBE = 10+10 =
$20
(4) [4 Marks] Market demand is Qd (P ) = 1000−10P . If there are currently 50 firms in the market,
∗ )?
what is the market price (PSR
Suggested Solution: In a competitive market, as the market price is a firm’s marginal benefit
of producing, the firm chooses the quantity where M C = P , this given a price P, it chooses qi
such that P = 10 + qi .
To find market supply, we need to sum each firm’s production at each price. This means we
need qi as a function of price. We thus invert P = 10 + qi to get qi (P ) = P − 10. As all firms
are identical, market supply as a function of price is Qs (P ) = 50 × qi (P ) = 50(P − 10). As
equilibrium equates quantities supplied and demanded:
Qd (P ∗ ) = Qs (P ∗ )
∗
∗
1000 − 10P = 50(P − 10)
P∗
20 −
= P ∗ − 10
5
100 − P ∗ = 5P ∗ − 50
equilibrium condition
substituting
150 = 6P ∗
P ∗ = 25
1
If you are a calculus freak, you could take the derivative of the AT C function with respect to qi and set it equal to zero,
then solve for qi .
20181119GazzaleRegular
Term Test 2: Solutions: Full
(5) [3 Marks] Your firm rents coffee roasting machines to firms that roast coffee. Given the short-run
with 50 coffee-roasting firms, explain whether you expect demand for coffee roasting machines
to increase or decrease. (Note: It is possible to get full marks for this question even if you did
none of the previous questions.)
Suggested Solution: You can get full marks even if you did not calculate whether the current
price is above or below the break-even price.
∗ >P
The general answer If PSR
BE , then the firms in the market are earning positive economic
∗ <
profits. This induces entry, which increases demand for coffee roasting machines. If PSR
PBE , then the firms in the market are earning negative economic profits. This induces exit,
which decreases demand for coffee roasting machines.
∗ >P
If you calculated prices PSR
BE , . . .
Importantly, if you miscalculated prices but your logic for this question is correct, you got full
marks.
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ANSWER TO A QUESTION REFERS US TO THIS PAGE.
20181119GazzaleRegular
Term Test 2: Solutions: Full