ECONOMICS I – ACADEMIC YEAR 2017-2018 TUTORIAL 3 – Government intervention, taxation, economic welfare TA: ANDREA VENEGONI EXERCISE 1. Consumer and Producer Surplus, Price Floors and Ceilings (14 pts) Suppose that in the Malaysian market of coconuts the demand function is Qd= 110-P and the supply function is Qs= -90+3P a. Calculate equilibrium price and quantity, consumer surplus, producer surplus and total economic welfare. Now suppose the government imposes a floor price of $60. b. Under the price floor how many coconuts will be sold? What will happen to consumer, producer surplus and overall economic welfare compared to the levels previously computed? Solutions: a) Recalling the equilibrium condition that wants Qd=Qs we can equate the two functions deriving the equilibrium price. 110-P=-90+3P 200=4P P*=50 By substituting the equilibrium price in either the demand or supply function we can compute the equilibrium quantity. For sake of computation simplicity we choose the demand function obtaining: Q*=110-50=60 To graph the outcome we have to compute the intercepts between the two curves and the axes. We start with the demand equation: To compute the intercept between the curves and the vertical (Y) axis we have to set Q=0 In this way we obtain: Demand: 0=110-P, and so, by taking P on the right side: P=110 Supply: 0=-90+3P , and so, by taking -90 on the right side: 90=3P, P=90/3=30 To compute the intercept between the curves and the vertical (Y) axis we have to set P=0 In this way we obtain: Demand: Q=110-0, and so, Q=110 Supply: Q=-90+0 , and so, Q=-90
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ECONOMICS I – ACADEMIC YEAR 2017-2018
TUTORIAL 3 – Government intervention, taxation, economic welfare
TA: ANDREA VENEGONI
EXERCISE 1. Consumer and Producer Surplus, Price Floors and Ceilings (14 pts)
Suppose that in the Malaysian market of coconuts the demand function is Qd= 110-P and the supply
function is Qs= -90+3P
a. Calculate equilibrium price and quantity, consumer surplus, producer surplus and total economic
welfare.
Now suppose the government imposes a floor price of $60.
b. Under the price floor how many coconuts will be sold? What will happen to consumer, producer
surplus and overall economic welfare compared to the levels previously computed?
Solutions:
a) Recalling the equilibrium condition that wants Qd=Qs we can equate the two functions
deriving the equilibrium price.
110-P=-90+3P
200=4P
P*=50
By substituting the equilibrium price in either the demand or supply function we can
compute the equilibrium quantity. For sake of computation simplicity we choose the
demand function obtaining:
Q*=110-50=60
To graph the outcome we have to compute the intercepts between the two curves and the
axes. We start with the demand equation:
To compute the intercept between the curves and the vertical (Y) axis we have to set Q=0
In this way we obtain:
Demand: 0=110-P, and so, by taking P on the right side: P=110
Supply: 0=-90+3P , and so, by taking -90 on the right side: 90=3P, P=90/3=30
To compute the intercept between the curves and the vertical (Y) axis we have to set P=0
In this way we obtain:
Demand: Q=110-0, and so, Q=110
Supply: Q=-90+0 , and so, Q=-90
b) To compute the new quantities demanded and supplied after the introduction of the price
floor of 90, it is sufficient to substitute, both in the demand and supply equation, the new
price level.
DEMAND: Qd=110-P Qd=110-60=50
SUPPLY: Qs=-90+3P Qs=-90+3*60=-90+180=90
So, to summarize, by recalling that the equilibrium quantity before the implementation of
the price floor was equal to 60, we have that such an intervention makes the quantity
demanded drop by 10 and the quantity supply increase by 30. This generates a surplus
(calculated as Qs-Qd) equal to 90-50= 40.
Y
DA
S
D
110
30
60
50
CS
PS
Y
DA
S
D
110
30
50
60
PRICE FLOOR
50 90
SURPLUS
CS
PS DWL
46.6
60
EXERCISE 2.
The US government is concerned about the high incidence of heart diseases among the
population.
Soft drinks demand in US is given by: Qd = 60 - 3P.
Soft drinks supply in US is given by: Qs =-20 + 5P.
To curtail junk food consumption, it is considering imposing a 2 dollars tax on soft drinks, the so
called sugar-tax.
a. (4 pts.) Calculate the market clearing price per pack and packs sold prior to the imposition
of the tax.
b. (6 pts.) Calculate the market clearing price and quantity after the imposition of the 10 euros
tax. Graph the outcome with and without the tax. What is the price that buyers pay and the
price that sellers receive with the tax?
c. (4 pts.) From your answers to (a) – (b) above, what is the incidence of the tax on consumers
versus producers, i.e. what proportion of the tax will consumers vs. producers pay?
d. (2 pts.) From your answer to (c ) above, what do you deduct about the relative elasticities of
buyers versus producers of liquors in US?
e. (4 pts.) Now calculate the incidence of the tax on buyers and sellers using the “pass
through” formula. (Hint: First calculate the elasticity of demand and supply at the market
equilibrium without the tax).
f. (4 pts.) Calculate total tax revenues to the US government from the tax and Dead Weight
Loss (DWL) associated with the tax and show them on the graph.
g. (4 pts.) Is the DWL larger or smaller than the tax? Discuss the implications of your findings.
Is this an effective tax? Why or why not? What considerations you believe are excluded
from this type of analysis.
Answer:
a. The market equilibrium price absent the tax is given by finding the P that equates Qd and Qs:
40 – P = -10 + 4P
50= 5P
P* = 10
The equilibrium quantity is given by plugging the equilibrium price into the Qd or Qs equation:
Qd = 40 –10 = 30
b. The tax of 2$ creates a wedge between the price buyers pay (Pb) and the price sellers
receive (Ps). Note that it does not matter to the market equilibrium whether the tax is
imposed on buyers or sellers of cigarettes.
Pb = Ps + 10
The demand and supply equations become:
Qd = 40 – Pb = 40 - (Ps + 2) = 40 – Ps - 2
Qs = -10 + 4Ps
The new market equilibrium will occur where Qd = Qs
40 - Ps - 2= -10 + 4Ps
48 = 5Ps
Ps = 9.6. This is the price sellers receive.
Pb = Ps + 2 = 9.6 + 2 = 11.6. This is the price buyers pay.
The new equilibrium quantity Q* is determined by substituting the new price paid by buyers Pb of
11.6 in the Qd equation or the new price received by sellers Ps= 9.6 in the Qs equation:
Qd = 40 – 11.6 = 28.4
Or alternatively,
Qs = -10 + 4(9.6) = 28.4
P
S
11.6
10 Old equilibrium without tax
9.6
D
28.4 30 Q
c. To calculate the proportion of the tax borne by buyers, we have to compare the price paid by
buyers with and without the tax. As a result of the tax, the market price went up by 1.6, from 10 to
11.6. Therefore consumers bear 1.6 of the 2 dollars of the tax or 80% of the tax. To calculate the
proportion of the tax paid by sellers, we have to compare the price received by sellers before and
after the tax. As a result of the tax, the price received by sellers fell from 10 to 9.6. Therefore,
sellers bear the remaining 0.4 dollars of the tax or 20% of it.
d. From (c ) above, buyers bear a significantly larger proportion of the tax than sellers. This implies
that the demand of buyers is less elastic (with regard to price) than the supply of sellers.
e. Pass-through formula: Es/(Es – Ed).
where Es = Elasticity of supply and Ed = elasticity of demand
It measures the incidence of the tax borne by buyers.