recap lecture 27 – academic year 2013/14 introduction to economics fabio landini
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Market of cheese
The market for cheese is characterized by the following demand and supply curve:
Demand: QD= 9 – P
Supply: QS= 3P – 3
where P represent the price (in Euro per Kg.) and Q represent the quantity (in Kg.).
Market of cheese
1) Compute the elasticity of demand with respect to price, for Δp=2 and assuming that p0 = 3.
Formula for the elasticity of demand:
ED(p) = – [Δ q / q0] / [Δ p / p0] =
= – [(q1 – q0) / q0] / [(p1 – p0) / p0]
Market of cheese
p0 = 3 ; p1 = p0+ Δp = 5
Given our demand function QD= 9 – P we can compute q0 and q1.
In particular:p0 = 3 -> q0 = 6
p1 = 5 -> q1 = 4
Market of cheese
Now we can apply the formula:
ED(p) = – [Δ q / q0] / [Δ p / p0] =
= – [(q1 – q0) / q0] / [(p1 – p0) / p0]= – [(4 – 6) / 6] / [(5 – 3) /3]
= – [– 1 / 3] / [2 /3]=1/2
Final result: ED(p) = 1/2
High or low? Low…
Market of cheese
2) Draw the demand & supply graph and find the equilibrium price and quantity
Price of cheese
Quantity of cheese
9
9
D1
12
5
S
88
To find the equilibrium price and quantity we impose the equilibrium condition:
QD = QS
QD = 9 – P and QS= 3P – 3
Therefore, 9 – P = 3P – 3, from which we get:
P= 3 and Q = 6
Market of cheese
Market of cheese
2) Suppose the EU imposes a minimum price equal to 5.
i) What is the effect on the market? Show graphically and analytically.
ii) Will the farmers agree with this intervention?
Market of cheese
i) Graphically,
Price of cheese
Quantity of cheese
9
9
D1
S
3
6 QS
5
QD
Excess supply
Market of cheese
We can use the supply and demand function to compute the size of excess supply
QD = 9 – P -> P=5 -> QD = 4QS= 3P – 3 -> P=5 -> QS = 12
The size of excess supply is
12 – 4 = 8.
Market of cheese
ii) To verify whether farmers agree with this intervention we compute the TR before and after the intervention
Before: TR = P x Q = 3 x 6 = 18
After: TR = P x Q = 5 x 4 = 20
Yes, farmers will support the intervention.
Market of cheese
3) In order to avoid excess supply the EU decides to introduce a tax T on producers. Which is the value of T such that excess supply is avoided?
i)Show the effect of the tax graphicallyii)Find the correct value of T
Market of cheese
ii) To find the correct value of T we write our new supply function
QD = 9 – P
QS= 3(P-T) – 3
To eliminate excess supply we have to satisfy the equilibrium condition QD = QS when P=5.
Market of cheeseTwo steps:First, we impose the equilibrium condition
QD = QS -> 9 – P = 3(P-T) – 3
Second, we replace P=5 and solve for T:9 – 5 = 3(5-T) – 3
7 = 15 - 3TT = 8/3
Market of cheese
i) Graphically,
Price of cheese
Quantity of cheese
9
9
D1
S
3
6 12
5
4
S’
Portion paid by consumers..
Portion paid by producers..
Market of cheeseThe portion paid by consumers is simply the difference between the new equilibrium price and the equilibrium price before the intervention, i.e. 5 – 3 = 2
For producer is the difference between the old equilibrium price and the new price that they receive, i.e.: 3 – (5 – 8/3) = 3 – 7/3 = 2/3
Obviously, the sum of the two portion gives us the tax burden, i.e. 2 + 2/3 = 8/3
Market of cheese5) Finally, evaluate the effect of the intervention in terms of allocative efficiency.
Does the intervention improve social welfare?
Show it graphically and analytically
Market of cheese
i) Graphically,
Price of cheese
Quantity of cheese
9
9
D1
S
3
6 12
5
4
S’
Producer surplus
Consumer surplus
Market of cheese
i) Graphically,
Price of cheese
Quantity of cheese
9
9
D1
S
3
6 12
5
4
S’
Producer surplus
Consumer surplus
Market of cheeseValue of Consumer Surplus (CS) and Producer Surplus (PS)
Before the intervention:CS = (6 x 6) /2 = 18PS = (6 x 2) /2 = 6 -> Total = 18+6 = 24
After the intervention:CS = (4 x 4) /2 = 8PS = {4 x [5 – (1+8/3)]} /2 = {4 x [5 – 11/3]} /2 = ={4 x 4/3} /2 = 8/3 -> Total = 6 + 8/3 = 26/3
Macroeconomic EquilibriumConsider an economy characterized by the following equations:•C = 1000 + 0,4YD
•I = 1000 – 5.000i + 0,1Y•T = 1000•G = 1200•MS/P = 600•MD = 0,2Y – 3.000i
Find the equilibrium level of income and interest rate.
Macroeconomic Equilibrium
The equilibrium condition in the goods market requires Y=Z:
Y = C + I + GY = 1,000 + 0.4YD + 1,000 – 5,000i + 0.1Y + 1,200
Y = 3,200 + 0.4(Y-1,000) – 5,000i + 0.1Y Y = 2,800 + 0.5Y – 5,000i
0.5 Y = 2,800 – 5,000i Y = 1,400 – 2,500i
Macroeconomic Equilibrium
The equilibrium condition in the financial market requires MS/P = MD:
600 = 0.2Y – 3,000i 0.2Y = 600 + 3,000i Y = 120 + 600i
Macroeconomic Equilibrium
Two equations with two unknowns:
Y = 1,400 – 2,500i -> Goods Market Y = 120 + 600i -> Financial Market
We can solve the system of equation to find the value of Y and i that satisfy the equilibrium conditions in both markets.
Macroeconomic Equilibrium
First we solve for i:
120 + 600i = 1.400 – 2.500i 3.100i = 1.280
i = 0.4129 We substitute for i in one of the goods market equation:
Y = 1,400 – 2,500i Y = 1,400 – 2,500 x 0.4129
Y = 367.75
Increase in public expenditure2) Using the AS-AD investigate the consequences of a fiscal policy in which public expenditure are increased. Explain the effect in the short period, during the transition, and in the medium period.
Increase in public expenditure( G )
Initially, let’s assume Y = Yn
Then, government reduces G
What are the short-period effects on equilibrium prices (P) and quantities (Y)? An what about the medium-period effects?
Increase in public expenditure
AS
AD
P
Y
A
Yn
AD’
A’
YA’
PA’
PA
G -> AD shifts rightwardEquilibrium A->A’ -> Y (YA -> YA’) P (PA -> PA’)
In A’ Y>Yn -> P>PE -> PE -> the transition starts
Y
During the transition -> Y and PIn the medium period -> YA’’ =Yn=YA and PA’’ >PA
AS
AD
P
A
Yn
A’
YA’
PA’
PA
PA’’
A’’
Total effects of the intervention:•Short period -> Y P•Transition -> Y P•Medium period -> Y= P
This is usually meant when it is argued that expansionary fiscal policy are inflationary in the medium period.
This result however is obtained under fairly stringent assumptions. For instance, G does not affect Yn (think
of public investments in scientific research)
Reduction of public deficit
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