ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
ECON1001D/E & 1210F/G: Introduction to Economics I Problem Set #04
Due: 11:30a.m. Tuesday April 22
Note:
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Both hand-written and computer-typed assignments are acceptable.
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Submit hard-copy only. Remember to staple your loose sheets.
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Late submission will not be accepted. Electronic submissions will not be accepted.
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Where to submit your assignment: KKL Building 9/F, drop-box with Grace and ECON1001D/E
ECON1210E/F. &
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Remember to write down your FULL name and University ID.
ECON1210F/G.
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Remember to write down your FULL name and University ID.
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1. Let’s assume that the market for dumpling is perfectly competitive. The City Government
decides to tax this delicious food item. The Council legislates that a $0.10 tax be paid on
each dumpling sold. (This is known as an excise or unit tax, as opposed to a sales or ad
valorem tax, which would be expressed in terms of percentage.)
a. Using two separate graphs, show the long-run equilibrium for the dumpling industry
and profits for a typical firm in this industry before the tax is imposed. Be sure to label
your graph carefully.
b. Explain and show graphically the short-run effects of the tax on the market for
dumpling on the cost curves of a typical firm, the industry supply curve, the industry
demand curve, and the equilibrium price and quantity in the industry.
c. Explain the effect of the tax in the short run on the profits of a typical firm.
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d. Explain and show graphically what will happen to this industry’s equilibrium price
and output, and to the profits of a typical firm in the long run (what happened to the
number of firms?) Assume this is a constant cost industry.
Solution:
a. The profit for each firm is zero (we assume that firms are exactly similar). Each firm is
producing at a level where P=AC (where total revenues are equal to total cost). This the
case in the long−run because positive (negative) profits for the typical firm would induce
some firms to enter (exit) the industry, which would shift market supply to the right (left)
and bring the price down (up) until profits are again zero. In this model, long−run
equilibrium can only happen at a price equal to the minimum of the average cost curve of
a typical firm.
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
b. Think of a unit tax ($0.10 per unit sold) as a vertical shift of 0.10 in a firm´s AC and MC
curves. Since the market supply is the sum of all MC curves, it also shifts vertically by
0.10, so price increases from P0 to P1. The important thing to note is that the price
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increases, but by less than 0.10. The market demand curve is unaffected by the tax, but
that does not mean that consumers would still buy the old quantity (Q0) at the new price.
Equilibrium quantity, for the market and each typical firm, decreases.
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
c. Each firm produces where new MR equals new MC. This occurs at a lower quantity, and
results in losses (the highlighted rectangle).
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d. If firms are making losses, some of them will exit the industry. Each time a firm exits, the
market supply curve shifts left, pushing the price up and reducing losses. This goes on
until profits are again zero; not surprisingly, at a price equal to the minimum of the new
AC curve. As the industry is a constant cost industry, market price has gone up by the full
amount of the tax, and market quantity has decreased. Remaining firms are producing the
same quantity they used to, but there are now less of them.
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2. The Utopian government has invited BITIC to build a bridge across a river under the
usual term of Build, Operate and Transfer (often, known as BOT,
http://en.wikipedia.org/wiki/Build-operate-transfer). Under the agreement, BITIC has to
build the bridge, operate for a year, and then transfer the bridge to the government. The
bridge costs $x to build and nothing to maintain. However, the bridge will last for only
two years (or it costs an astronomical amount to maintain after the first two years). It is
possible (and common) for the government to give a lump-sum subsidy or concession of
$y to BITIC. Suppose the toll collection costs $1 per crossing, and the following equation
shows the company's anticipated number of crossings in a typical year at different tolls:
P = 8 – 0.01Q
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
where P denotes the toll per crossing, and Q the number of crossings in thousands. For
instance, when the toll is $7, we will have 7 = 8-0.01Q, Q = 100. i.e. 100 thousand
crossings.
a. Once the bridge is built, what would be its profit-maximizing toll? What is the usage
of the bridge (number of crossing)?
b. Is the usage in part (a) socially efficient? Explain.
c. Suppose the cost of building the bridge is $2 millions (i.e., x = 2 million). What must
be minimum amount of subsidy from the government so that BITIC will be interested
in building the bridge?
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d. Assuming that the bridge has been built and transferred to the government. What level
of toll would you expect the government to charge after it takes over the bridge?
Solution:
a. The profit-maximizing toll is $4.5 and the usage is 350 thousands crossings.
If the demand curve is a straight line, then the marginal revenue curve is a straight line
that begins at the same point on the vertical axis as the demand curve but with twice the
slope. Thus, given the demand curve is P=8-0.01Q, we know that the MR curve is
MR=8-0.02Q.
To maximize profit, a firm should produce until marginal revenue equals marginal cost
(MR=MC). Since MC=$1, we can substitute MR=1 into the marginal revenue equation:
1=8-0.02Q, Q=350.
As the profit-maximizing output will be 350, we can substitute Q=350 into the demand
equation P = 8 – 0.01*350. So the profit-maximizing toll will be $4.5.
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b. This level of usage is not efficient.
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
From the society's perspective, we should continue to expand output as long as the value
of an additional unit is higher than the marginal cost of producing the good. At the
monopoly's output (Q=350), the value of an additional unit (a point on the demand curve)
is $4.5 (the price charged by the monopoly), while the marginal cost of production is $1.
So the monopoly's output is not socially efficient.
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c. BITIC would be interested in building the bridge only if the subsidy is larger than
$775,000.
When BITIC builds the bridge, it can earn a revenue of P*Q = $4.5*350,000 =$1,575,000.
It also incurs a fixed cost of $2 millions and variable costs of MC*Q = $1*350,000 =
$350,000. In total, its loss generated will be equal $2 millions + $350,000 - $1,575,000 =
$775,000.
Therefore, the amount of subsidy from the government should at least be able to cover its
loss (i.e. $775,000), otherwise BITIC would not be interested in building the bridge.
d. The price charged by the government is $1 or $0.
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
After the bridge is transferred to the government, it will choose its output level to be the
same as the socially efficient output, i.e. 700. This is because when the government
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operates the bridge, it does not need to maximize profit. A government would only want to
maximize the total economic surplus in the market. It may also have the objective of
encouraging traffic. Therefore, the price charged by the government should be $1, which
is the same as marginal cost.
In this case, total economic surplus is equal to (($8 - $1)*700,000)/2 = $2,450,000.
Here is an alternative answer that is also acceptable. Suppose the government charge zero
toll. Then, there is no need to incur a cost of collecting the toll. That is, the marginal cost
of additional crossing is zero. Then, the usage can be found to be 800 by setting P=0.
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
In this case, since we can save on the manpower of collecting the toll, total economic
surplus will be even bigger, which is equal to ($8*800,000)/2 = $3,200,000.
3. A monopoly faces market demand Q=30−P and has a cost function C(Q) = Q2/2,
MC(Q)=Q.
a.
What is the socially optimal price? Calculate consumer surplus (CS) and producer
surplus (PS) for the monopoly, and the deadweight loss (DWL) due to the monopolist
behavior of this firm. Show the monopoly CS, PS, and DWL on the diagram.
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b.
Find the profit maximizing price and quantity and the resulting profit to the
monopoly.
c.
Assume that the government puts a price ceiling on the monopolist at P = 18. How
much output will the monopolist produce? What will be the profit of the monopolist?
Calculate CS, PS, and DWL. Why is the deadweight loss different now?
d.
Assume that the government put a price ceiling on the monopolist in order to
maximize the total (i.e. consumer plus producer) surplus. What price ceiling should it
choose? How much output will the monopolist produce at this price ceiling? What
will the profit of the monopolist be? What is the DWL?
Solution:
a. Given the demand curve is P=30-Q, we know that the MR curve is MR=30-2Q. To
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
maximize profit, a firm should produce until marginal revenue equals marginal cost
(MR=MC). Since MC=Q, we can equate 30-2Q=Q, QM=10.
As the profit-maximizing output will be 100, we can substitute Q=10 into the demand
equation P = 30-Q. So the profit-maximizing price will be PM=20.
The profit = P*Q - Q2/2 = 20*10 – 10*10/2=150.
The socially optimal equilibrium should be the intersection when demand curve
intersects with supply curve (MC). That is, 30-Q = Q. So socially optimal quantity
QS=15 and socially optimal price PS=15.
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b.
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As the figure above, at the socially optimal equilibrium, PS is the green area, which is
equal to 15*15/2=112.5. CS is the blue area, which is equal to 15*(30-15)/2=112.5. So
total economic surplus under socially optimal equilibrium should be 225.
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ECON1001D/E & 1210F/G: Intro to Econ I Problem Set #4
For the monopoly, as the figure above, PS is the green area, which is equal to
[(20-10)+20]*10/2=150. CS is the blue area, which is equal to 10*(30-20)/2=50. So total
economic surplus under monopoly should be 200.
The DWL due to the monopolist behavior of this firm should 225-200 = 25, which is
represented by the red shaded area.
Because the monopoly price yields the highest profit for the monopoly, the closer price
to the monopoly price, the higher profit. If the government sets a price ceiling of P=18,
the monopoly should set the optimal price at P=18 as well, so that can maximize its
profit under price ceiling.
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c.
d.
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As the figure showed above, at P=18, quantity demanded Q=12, according to the demand
curve. So CS=12*(30 – 18)/2 = 72, represented by blue area. PS = (18-12+18)*12/2 =
144, represented by green area. DWL = 225 – 72 – 144 = 9, represented by red area.
Because the price is closer to the socially optimal price, part of the PS transfers to CS,
and total economic surplus increases. So DWL decreases.
Because at the socially optimal equilibrium, total economic surplus is maximized (there is
no DWL), so the price ceiling should be P=15, which is also the socially optimal price.
From the demand curve, at P=15, the monopolist should produce Q=15. Profit = 15*15 –
15*15/2 = 112.5. There is no DWL.
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