Answers to ECMC02 First Test, October 28, 2006
1. Demand is P = 50  .015Q.
Supply is P = 10 + .005Q.
These intersect
where 50  .015Q = 10 + .005Q, or 40 = .020Q, so Q* = 2000.
Substituting into the demand curve we have P* = 50  .015(2000) =
$20.
The consumer surplus is given by the area under the demand
curve but above the price line, which is (50 – 20) x 2000/2 = $30,000.
The correct answer is (I).
2. Producer surplus is given by the area below the price line and above
the MC or supply curve, which is (20 – 10) x 2000/2 = $10,000.
The
correct answer is (D).
3. If the number of taxi rides per day is restricted by quota to 1000
rides, the going price will be P = 50  .015(1000) = $35.
The cost to
producers of providing this number of taxi rides is given by the
original supply curve, or P = 10 + .005(1000) = $15.
The new producer
surplus is given by the area below the new price line and above the
supply curve, so it is [(35 – 15) x 1000] + (15 – 10) x 1000/2 = $22,500.
The correct answer is (H).
4. The quota restricts output to 1000 rides per day.
The areas of
consumer surplus and producer surplus that originally existed beyond
1000 rides per day are lost to society because of the quota.
Therefore, the deadweight loss is (35 – 15) x (2000 – 1000)/2 =
$10,000.
The correct answer is (D).
5. The new purchasing policy will expand producer surplus, but it will cost
a substantial amount of wasted government revenue.
The net of these
two provides the measure of deadweight loss.
First, we must
determine how much additional purchasing takes place.
The question
says that price will be kept up at the “quota” level from Question 3,
which is $35.
From the supply curve, we can see that this means that
$35 = 10 + .005Q, so that Q = 25/.005 = 5000 units.
Private demand
for taxi rides at this price will be 1000 units, as we know from the
answers above.
Therefore, the government will have to purchase
4000 taxi rides to keep price at this level.
The additional producers
surplus will be 4000 x (35 – 20)/2 = $30,000.
However, the wasted
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cost of these taxi rides will be 4000 x $35 = $140,000.
The net
amount of deadweight loss is therefore $110,000.
The correct
answer is (U).
6. If demand is P = A – bQ, then MR = A – 2bQ.
MC = dTC/dQ = c.
The
monopoly firm will profitmaximize by setting A – 2bQ = c, so the
equilibrium quantity traded will be Q* = (Ac)/2b.
The profit
maximizing price will be given by substituting this into the demand
curve, so P* = A – b((Ac)/2b) = A – A/2 + c/2 = A/2 + c/2 = (A + c)/2.
The correct answer is (F).
7. The amount of deadweight loss is given by comparing the monopoly
result with the perfectly competitive result.
The perfectly
competitive result would be where P = MC or A – bQ = c, or Q = (A –
c)/b.
The amount of lost production due to monopoly is therefore (A –
c)/b – (A – c)/2b.
The amount of deadweight loss is [(A + c)/2 – c] x
[(A – c)/b – (A – c)/2b]/2 = [(A  c)/2] x [(A – c)/2b]/2 = (A – c)
2
/8b.
The correct answer is (C).
8. If b were twice as large, the denominator would be multiplied by 2.
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 Fall '08
 CLEVELAND
 Supply And Demand, Correct Answer, producer

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