Linear demand and supply functions: calculating the effects of subsidies on
markets and community welfare
1: Suppose we are given the following demand and supply functions:
Qd = 60 – 2P
Qs = -20+ 2P
(a) Solve for the equilibrium price and quantity.
(b) Plot the two curves on a coordinate map.
Suppose the government grants a subsidy of $4 per unit. This means that the
supply curve will shift downwards by $4 for each level of output.
The new supply curve S2 (S1 - subsidy) lies below the initial supply curve S1.
Just count $4 down along the vertical axis from the y-intercept of 10. We find
that the y-intercept of S2 is 6. Now draw a line parallel to S1 – this gives you the
new supply curve.
2: How to find the new price paid by consumers, the price received by producers
and the quantity bought and sold following the granting of a subsidy. To get
accurate values, we must find the new post-subsidy supply function, solve for Pc
and Qsub and then use Pp = Pc + subsidy per unit to find Pp.
Given a supply function of the general form Qs = c + dP, whenever there is
an downward shift of the function by s units, where s = subsidy per unit, we
replace P by P + s. The new supply function becomes Qs = c + d (P +s)
We can now use this rule to find the new supply function. Our initial supply
function was Qs = -20 + 2P. With a subsidy of $4 per unit, this function shifts
downwards by $4, so that s = 4. Therefore the new supply function becomes:
Qs = -20 + 2(P + 4)
Simplify to find the new supply function.
Plot the new supply function on the diagram
3: Now use the original demand function and new supply function to solve for
equilibrium price and quantity
Qd = 60 – 2P
Qs =
4: The following question comes from the website
http://www.econclassroom.com/wpcontent/uploads/2011/11/GovernmentInterventionPracticeCalculatingtheeffectsofsubsidies.pdf [accessed November 29 2014]
Assume the supply and demand for petrol in China is represented by the
following equations:
● Qs = -200 + 100P
● Qd = 1,000 - 200P
where Qs is the quantity supplied (in millions of litres) by Chinese petrol firms
and Qd is the quantity demanded (in millions of litres) by Chinese petrol
consumers. P is the price per litre for petrol expressed in Chinese yuan.
a) Illustrate the market for petrol in China in equilibrium assuming no
government intervention.
b) Calculate the equilibrium price and quantity of petrol in China, and label
them on your graph.
c) Calculate the amount of consumer and producer surplus in the Chinese
petrol market. Add these together to determine the amount of total
welfare (economic surplus) in the petrol market.
d) Assume that the government wishes to make petrol more affordable to
Chinese consumes, so it provide a 1 yuan subsidy per litre for petrol
producers. Derive the new supply equation for petrol in China.
e) Plot the original supply and demand curves, then show the effect of the 1
yuan subsidy for petrol producers.
f) Calculate the new equilibrium price consumers will pay for petrol and the
new equilibrium quantity of petrol produced. Calculate the price that
petrol producers will receive following the 1 yuan subsidy. Indicate these
on your graph.
g) Calculate each of the following:
a. the new area of consumer surplus that will result from the petrol subsidy.
b. the new area of producer surplus following the subsidy.
c. The net increase in consumer and producer surplus resulting from the subsidy.
(h) Calculate the cost the subsidy imposes on taxpayers in China.
(i)
Compare the cost you calculated in number 8 to the net increase in
consumer and producer surplus you calculated in 7,c). What does
the difference between these two figures represent?
(j) On the graph you drew in #5, shade and label the area that represents the net
effect on total welfare (economic surplus) of the subsidy. Does this represent an
increase or a decrease in overall
efficiency in the petrol market? Explain.