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Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
Problem Set #3: Welfare, Externalities and Public Goods
Due August 8th, 2014
1. Coffee, Welfare and Elasticity: Suppose the demand for packaged coffee is given by:
QD= 15-0.5P and the supply of packaged coffee is given by: QS=P
a. Plot the demand and supply curves on the same graph. Find the equilibrium
graphically and algebraically: what is the equilibrium price and quantity of coffee?
P
30
S
P*=10
Q*=10
D
15
Q
Algebraically:
In equilibrium: QD  QS
15 - 0.5P = P
15 = 1.5P
P*=10
Q*=10
b. At this equilibrium, calculate consumer surplus (CS), producer surplus (PS), and
social surplus (SS).
CS is the area below the demand curve and above the price consumers pay. That
is: CS = [$10* (30-10)]/ 2 = $100
PS is the area above the supply curve and below the price producers keep. That
is: PS = [$10* (10-0)]/2 = $50
SS is the sum CS and PS, or $150.
c. Now assume coffee producers lobby the government to institute a price floor of $12.
What will be the new price and quantity of coffee transacted in the market? The new
CS, PS, and SS?
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
With price floor of $12, quantity supplied will exceed quantity demanded.
Specifically, QS=12, QD=9 (using the supply and demand equations). Thus 9
units are transacted in the market. The price will be $12. See the graph below.
The new CS is 0.5*9*$18 = $81 (the triangle above the price floor and below
demand) and the new PS is the quadrilateral under the price floor and above
supply between Q=0 and Q=9. The area of this can be calculated by adding the
area of the triangle and the rectangle that make up the quadrilateral, so: PS=
0.5*9*$9 + $3*9 = $40.50 + $27 = $67.50. Thus SS = $81 + $67.50 = $148.50.
d. Who gains and who loses from the price floor? What is the DWL from the price
floor?
We can see from CS and PS that consumers lose and producers, on the whole,
gain (CS fell but PS rose). Overall though, we have a DWL of $1.50, since SS fell
by $1.50. This is the area of the triangle to the left of the old equilibrium,
between Q=9 and Q=10.
e. In one sentence ONLY, explain what DWL is in this specific case - what is actually
lost?
DWL comes from lost consumer and producer surplus that could have been
obtained if the 10th unit was produced and consumed.
f. Calculate the elasticity of demand when the price increases from the equilibrium price
found in (a) to $12. Is it elastic or inelastic demand?
When the price was $10, the quantity demanded was 10. When the price is $12,
the quantity demanded is 9.
(Q2  Q1 ) /(( Q1  Q2 ) / 2)
( P2  P1 ) /(( P1  P2 ) / 2)
(9  10) / 9.5
eD 
 0.578
(12  10) / 11
eD 
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
Demand is inelastic because it is smaller (in absolute value) than one. The percentage
change in quantity is smaller than the percentage change in price.
2. Externalities in Gnomeland
a. In Gnomeland, externalities pervade in four markets (listed below). For each, state the
kind of externality that exists.
i.
A local seafood restaurant is incredibly popular with the town, and is especially
loved for its fried calamari. However, the restaurant’s surrounding neighbors
complain that whenever the chefs are cooking, they cannot rid their homes of the
unpleasant, fishy aroma. Negative production externality
ii.
A parking lot, which offers parking space for up to 100 residents and visitors of
Gnomeland. However, during peak hours (9 AM and 5 PM) the sound of honking,
breaking, and traffic disturbs area gnomes. Negative consumption externality
iii. A vaccination for swine flu, which makes individuals immune against the illness.
Positive consumption externality
iv.
A florist, who provides wonderful bouquets and floral arrangements for many
Gnomeland festivities, has a beautiful garden where he grows all of his flowers.
Many gnomes enjoy passing the garden and admiring its beauty as they walk
through town. Positive production externality
b. Draw a well-labeled graph for each of the four markets described above. Be sure to
include and label S, D, MPB, MPC, MSB, MSC, Qmkt (the market quantity), Qeff (the
socially optimal quantity) and DWL.
(1) [Negative Production Externality (Restaurant)]
P
MSC
DWL
S=MPC
D=MSB=MPB
Q efficient
Q mkt
Q
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
(2) [Negative Consumption Externality (Parking lot)]
Price
S = MPC = MSC
DWL
D = MPB
MSB
Qeff Qmkt
Quantity
(3) [Positive consumption externality (swine flu vaccination)]
Price
S= MPC = MSC
DWL
MSB
D = MPB
Qmkt
Qefficient
(4) [Positive Production Externality (Florist)]
Quantity
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
S=MPC
DWL
MSC
D=MSB=MPB
Qmkt
Q eff
Q
c. In which markets would the government consider implementing a tax? Which might they
subsidize?
They may tax the restaurant owners or the parking lot customers. They may
subsidize swine flu vaccinations or the florist’s business.
3. Public Goods: Suppose there are two people in a society – a hawk and a dove. The hawk
wants to spend lots of money on national defense systems (a public good), whereas the dove
is less keen on doing this. The demand curves for single “units” of national defense for the
two different individuals are given as follows:
The “hawk”: QD=500-10P
The “dove”: QD=100-10P
Suppose that the marginal cost (or the "price") of a unit of national defense is constant at $50.
a. Does any single individual have an incentive to buy a unit of national defense?
No individual person is willing to pay $50 or more for a unit of national defense.
Since a unit costs $50, no individual has any desire to buy a unit on their own.
b. Draw the demand curve for national defense for all people in the society.
See graph below, derived by adding the demand curves for the two individuals
vertically:
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
c. What is the socially optimal number of units of national defense?
At a price of $50, the number of units of defense can be seen graphically below: