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Elasticities, Indirect taxes and subsidies. Test answers and comments
General comments:
 As I had already mentioned in class, except for the last question, your answers should
be in essay form, which means that a simple list of points is not enough.
 Abbreviations such as P or Q are only accepted in the diagram: your answers should
include full words, so supply (not S!), demand (not D!) and so on.
1. Define ‘cross price elasticity of demand’ (XED) and, using examples, explain the factors
that cause XED to have a positive, negative or zero value. (8 marks)
Definition. Check your textbook.
Although the question did not ask explicitly for the formula of the XED, you were supposed
to give either the formula or an explanation of how the XED is calculated.
The explanation of the possible values is in your textbook. I only include one below as an
example:
When the two goods considered are substitutes, there is a direct relationship between the
change in the price of one and the change in the quantity demanded of the other good. This
implies that numerator and denominator will have the same sign and the XED will be
positive. For instance, if the price of apples increases (positive denominator), the quantity
demanded of pears will increase (positive numerator), and the XED between apples and pears
will be larger than zero. Hence, when two goods are substitutes, the XED is larger than zero.
2. Using an appropriate diagram, explain how subsidies may lead to misallocation of
resources and allocative inefficiency. (10 marks)
This question was almost identical to the one we did during the lesson, in which I used
Abdullah’s answer to show you how you are supposed to answer this type of questions. It was
quite disappointing to see that many of you still failed to answer.
A subsidy is a payment made by the government to firms for the purpose of increasing
production, lowering costs or protecting against foreign producers. In this case, we will refer
to subsidies as an amount of money paid to firms per unit of output produced. For example,
consider the case of subsidies given to firms producing solar energy panels.
(Now you should explain what misallocation of resources is, so you first should explain what
allocative efficiency is)
Allocative efficiency occurs when the economy produces the combination of goods that are
mostly wanted by society. That is, when the ‘what to produce’ question is answered in the
best possible way. In a competitive market, allocative efficiency is achieved at the equilibrium
point, where quantity demanded is equal to quantity supplied and marginal benefit (given by
the demand curve), MB, is equal to marginal cost (given by the supply curve), MC. Whenever
this condition is not met, there is over- or underallocation of resources to the production of the
good, meaning that either too much or too little of the good is being produced.
When a subsidy is provided, it has the effect of lowering producers’ costs, which is one of the
non-price determinants of supply. As a consequence, supply will shift to the right, as the
minimum price producers are willing to accept in order to produce each level of output is
lowered by the amount of the subsidy. As shown in the diagram below, the vertical distance
between the old supply curve S1 and the post-subsidy supply curve S2 is equal to the amount
of the subsidy.
Market for solar panels
P
S1=MC
Subsidy
per unit
PP
S2= S1 - subsidy
MC(Qsb)
MB(Qsb)
PC
D=MB
Q*
Qsb
Q
As a result, a new equilibrium arises, with a lower price paid by consumers (PC), a larger price
received by producers, PP, and a larger equilibrium quantity Qsb. However, at the new
equilibrium quantity Qsb, marginal cost, which is given by the original supply curve, is larger
than marginal benefit, as the diagram above shows. That is, the extra cost to society of
producing one more unit of output is larger than the extra benefit from consuming an extra
unit. Society would be better off if less of the good was produced. In other words, in the postsubsidy equilibrium there is overallocation of resources to the production of the good and
allocative inefficiency.
3. Using examples, explain two determinants of price elasticity of supply. (4 marks)
Here you were supposed to give a general explanation of the determinant, at least an example
and a description of how the determinant affects the price elasticity of supply. I include the
following as an example. You can check the rest in your textbook/handout.
Spare capacity of firms. This refers to capacity of firms which is not being used. That is, the
firm might have some idle resources, such as unused machines or buildings. If a firm has
some unused capacity, then it will be easier to respond to a price increase with a larger
quantity of output. The larger the spare capacity, the larger the price elasticity of supply.
4. The demand and supply functions for good Zeta are given by Qd = 10-4P and Qs = -2 + 8P,
where Qd and Qs are quantity demanded and supplied respectively in units per day, and P is
the price of Zeta in $. The initial equilibrium values for price and quantity are P*= 1 and Q*=
6.
a) Graph the demand and supply curves and identify the initial equilibrium. (2 marks)
b) The government imposes an indirect (excise) tax of $0.75 per unit of Zeta. State the new
supply function and draw the new, post-tax supply curve in your diagram. (3 marks)
New Supply function: Qs= -2 + 8(P–0.75). That is: Qs=-8+8P.
c) Calculate the post-tax equilibrium price and quantity in the Zeta market. (2 marks)
Solving 10-4P=-8+8P for P you obtain: P=1.5. Substituting in either the demand or supply
function gives Qtax=4.
d) State the price paid by consumers and the price received by producers and show them in
your diagram. (2 marks)
Pc=1.5
Pp=1.5-0.75=0.75
e) Calculate government revenue from the tax. (1 mark)
Qtax *Tax= 4*0.75=3
f) Calculate the tax incidence on consumers and on producers. (2 marks)
Tax burden for consumers = (Pc-P*) x Qtax =(1.5-1) 4=2
Tax burden for producers =(P*-Pp) x Qtax = (1-0.75) 4=1
4. The demand and supply functions for good Zeta are given by Qd = 10-P and Qs = -4 + P,
where Qd and Qs are quantity demanded and supplied respectively in units per day, and P is
the price of Zeta in $. The initial equilibrium values for price and quantity are P= 7 and Q= 3.
a) Graph the demand and supply curves and identify the initial equilibrium. (2 marks)
b) The government imposes an indirect (excise) tax of $2 per unit of Zeta. State the new
supply function and draw the new, post-tax supply curve in your diagram. (3 marks)
c) Calculate the post-tax equilibrium price and quantity in the Zeta market. (2 marks)
d) State the price paid by consumers and the price received by producers and show them in
your diagram. (2 marks)
e) Calculate government revenue from the tax. (1 mark)
f) Calculate the tax incidence on consumers and on producers. (2 marks)