IB ECON GR 11 WK 8
CALCULATING SUBSIDIES
Subsidies can be calculated using D + S linear functions
Suppose the D + S for Rice is represented by the following functions. Rice quantity is
in Kg per day and price is expressed in Yuan.
Qd= 60-2P
and
Qs = -20 + 2P
a. Identify the Q intercept for D curve = ___________________________________
b. Identify the P intercept for D curve = ___________________________________
c. Identify the Q intercept for S curve = ___________________________________
d. Identify the P intercept for S curve = ____________________________________
e. Find the equilibrium P and Q the lot the curves in the space below
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IB ECON GR 11 WK 8
Assume the government grants a subsidy of Yuan 4 per unit of output – this leads to shift
in the S curve to the right to S - subsidy.
HOW DO WE PLOT THE NEW S CURVE AFTER THE SUBSIDY?
1. Move downwards by Yuan 4 along the P intercept of S curve – if the intercept was
(0, 10) then new S-sub curve P intercept = (0, 6) parallel to S.
2. Find the following info:
3.
i.
new Pc paid by consumers after subsidy
ii.
new Pp received by producers after subsidy
iii.
new Q bought after the subsidy
iv.
new Q sold after the subsidy
HOW?
To get set values of new S and D curve intersection we follow this rule:
Given a S function Qs = c + d P, whenever, there is a downward shift (right shift) of
the S function due to a subsidy; we replace P by (P + S)
New S function
Qs = c+ d (P + S)
Find the new S function
______________________________________________
______________________________________________
______________________________________________
4. Use the D function and the new S function to find new equilibrium P and Q
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IB ECON GR 11 WK 8
5. Identify the P paid by consumers and P received by producers after subsidy
P paid by consumers (Pc) = __________________________________________
P received by producers (P p) = _______________________________________
(Pc + Sub)
CALCULATING THE EFFECTS OF SUBSIDIES ON MARKET OUTCOMES AND
SOCIAL WELFARE

After subsidies consumers paid lower P (from --------- to ----------)

After subsidies producers received higher P (from --------- to ----------)

Q consumed and supplied increased (from --------- to ----------)
Therefore we need to use P & Q information and graph to calculate the following:
i.
Consumer Expenditure
ii.
Producer Revenues
iii.
Government Expenditure
iv.
Consumer Surplus
v.
Producer Surplus
1. CONSUMER Expenditure: Price paid per unit X Quantity bought

Before the subsidy- Consumers spent= Pe X Qe
_________________________________________________________

After the subsidy – Consumers spent = Pc X Qsub
_________________________________________________________

Consumer expenditures increased by
________________________________
2. PRODUCER Revenues:

Price received per unit X Quantity sold
Before the subsidy – producers received = Pe X Qe
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IB ECON GR 11 WK 8
_________________________________________________________

After the subsidy – producers received = Pp X Qsub
_________________________________________________________

Producer revenue increased by __________________________________
3. GOVERNMENT EXPENDITURE: 2 methods of calculation
a) Subsidy per unit (Pp – Pc) X Units sold (Qsub)
____________________________________________________________
b) Revenues = difference between producer revenues and consumer expenditure
after the subsidy
___________________________________________________________
Showing CS and PS on a Graph:

CS = area above Pe and under demand curve and up to Qe

PS = area below Pe and above supply curve and up to Qe
In a competitive market Social Surplus (total CS + PS) is maximum indicating allocative
efficiency (MB = MC) at point of eq’b.
DRAW WHAT HAPPENS TO SOCIAL SURPLUS Bf/After SUBSIDY
After
Before
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IB ECON GR 11 WK 8

After the subsidy - both consumer and producer surplus increased.

CS is area under D curve and above Pc up to o/p Qsub. : Consumer gain = shaded
area “gain in consumer surplus”

PS area above S curve S-sub and below Pp up to o/p Qsb : producer gain = shaded
area “gain in producer surplus”

Government loses due to negative effect on budget (opportunity cost of spending on
alternatives) i.e. the cost to government = (Pp – Pc) X Qsub

Social loss to government is the small welfare triangle (taxpayers not consuming
good)
Why does the dead weight loss occur?
Dead weight loss occur because subsidy causes the market to produce more than optimal
quantities (Qsub > Q*). The subsidy leads to overproduction of the good compared to what
is desirable by society – over allocation of resources or allocative inefficiency.
CALCULATING THE EFFECTS OF SUBSIDY ON CONSUMER AND PRODUCER
SURPLUS
1. Calculating CS before subsidy:
(P intercept of D – Pe paid by consumers)
X
Qe purchased
2
2. Calculating CS after subsidy:
(P intercept of D – Pc paid by consumers)
2
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X
Qsub purchased
IB ECON GR 11 WK 8
3. Calculating PS before subsidy:
(Pe of producer – P intercept of S)
X
Qe purchased
2
4. Calculating PS after subsidy:
(Pc – P intercept of Ssub )
X
Qsub purchased
2
HOW TO CALCULATE WELFARE LOSS AFTER SUBSIDY
Welfare loss can be calculated by taking pre subsidy sum of CS and PS (total social
benefits) and subtracting the post subsidy social benefits.
Welfare Loss = PS + CS – government expenditure on the subsidy
OR it can be calculated by:
(Pp – Pc) (Qsub - Qe)
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