Step by Step Guide for Quantitative Methods for Economists Exam
SECTION A (MATHEMATICS)
Answer TWO questions from this section
(Ensure you show your workings)
1. The demand and supply functions of a good are given by:
𝑄𝐷 = 50 − 2𝑃,
𝑄𝑆 = 10 + 𝑃,
where 𝑃, 𝑄𝐷, and 𝑄𝑆 denote price, quantity demanded and quantity supplied, respectively.
a) Find the equilibrium price and quantity (5 marks)
Equilibrium price and quantity is where the quantity supplied in the market is equal to quantity
demanded. This is the point where all the demand is satisfied and the market clears fully, so there is
no excess demand or excess supply. So you set Qs = Qd:
Qs = Qd
10 + P = 50 – 2P
Now rearrange to get P on its own to find the value of P:
3P = 40
P = 13.33
Now since we have found the value of P, we can substitute this number into either Qd or Qs to find
the value of Q, so substitute P = 13.33 into Qs:
Qs = 10 + P
Qs = 10 + 13.33
Qs = 23.33
So the equilibrium price and quantity is Price = £13.33 and Quantity is 23.33 units.
b) Draw a graph for the demand and supply functions, and show the equilibrium price and
quantity (8 marks)
To be able to draw the demand and supply functions, we need to know whether they are upwards or
downwards sloping and where they cross the x and y axis. The Law of Demand states that as price
increases, Quantity demanded decreases, so this is a negative relationship between price and
quantity so it has a negative slope so from left to right it’s going downwards. The Law Of Supply
states that as supply increases, Quantity Supplied also increases so this is a positive relationship
between price and quantity so it has a positive slope so it’s going upwards.
To find the intercepts, we need to set both Qs and P to zero to find the corresponding values:
For the demand function, Qd = 50 – 2P
If we set P to be zero, we will be able to find where it crosses the x axis:
Qd = 50 – (2x0)
, Step by Step Guide for Quantitative Methods for Economists Exam
Qd = 50
So the x intercept is 50
Now set Qd to zero, to find where it crosses the y axis:
0 = 50 – 2P
Rearrange to get P on its own to find the value of P
2P = 50
P = 25
So the y intercept is 25
Now do the same for Qs, so set P to zero to find the x intercept:
Qs = 10 + P
Qs = 10 + 0
Qs = 10
So the x intercept is 10
Now set Qs to zero to find where it crosses the y axis:
0 = 10 + P
-10 = P
So the y intercept is -10
Now you can plot these four points and join the points together to get:
You’ll know if you’ve done it right the
two lines cross at the points of
equilibrium that we found earlier: P =
13.33 and Q = 23.33
c) Calculate the price elasticity of demand at equilibrium. (5 marks)
Price elasticity tells us how the consumer responds to a change in price of a good. The question asks
for the price elasticity of demand at equilibrium, so we use the figures for Price and Quantity we
calculated at equilibrium, so P = 13.33 and Q = 23.33 and substitute these into the PED formula:
SECTION A (MATHEMATICS)
Answer TWO questions from this section
(Ensure you show your workings)
1. The demand and supply functions of a good are given by:
𝑄𝐷 = 50 − 2𝑃,
𝑄𝑆 = 10 + 𝑃,
where 𝑃, 𝑄𝐷, and 𝑄𝑆 denote price, quantity demanded and quantity supplied, respectively.
a) Find the equilibrium price and quantity (5 marks)
Equilibrium price and quantity is where the quantity supplied in the market is equal to quantity
demanded. This is the point where all the demand is satisfied and the market clears fully, so there is
no excess demand or excess supply. So you set Qs = Qd:
Qs = Qd
10 + P = 50 – 2P
Now rearrange to get P on its own to find the value of P:
3P = 40
P = 13.33
Now since we have found the value of P, we can substitute this number into either Qd or Qs to find
the value of Q, so substitute P = 13.33 into Qs:
Qs = 10 + P
Qs = 10 + 13.33
Qs = 23.33
So the equilibrium price and quantity is Price = £13.33 and Quantity is 23.33 units.
b) Draw a graph for the demand and supply functions, and show the equilibrium price and
quantity (8 marks)
To be able to draw the demand and supply functions, we need to know whether they are upwards or
downwards sloping and where they cross the x and y axis. The Law of Demand states that as price
increases, Quantity demanded decreases, so this is a negative relationship between price and
quantity so it has a negative slope so from left to right it’s going downwards. The Law Of Supply
states that as supply increases, Quantity Supplied also increases so this is a positive relationship
between price and quantity so it has a positive slope so it’s going upwards.
To find the intercepts, we need to set both Qs and P to zero to find the corresponding values:
For the demand function, Qd = 50 – 2P
If we set P to be zero, we will be able to find where it crosses the x axis:
Qd = 50 – (2x0)
, Step by Step Guide for Quantitative Methods for Economists Exam
Qd = 50
So the x intercept is 50
Now set Qd to zero, to find where it crosses the y axis:
0 = 50 – 2P
Rearrange to get P on its own to find the value of P
2P = 50
P = 25
So the y intercept is 25
Now do the same for Qs, so set P to zero to find the x intercept:
Qs = 10 + P
Qs = 10 + 0
Qs = 10
So the x intercept is 10
Now set Qs to zero to find where it crosses the y axis:
0 = 10 + P
-10 = P
So the y intercept is -10
Now you can plot these four points and join the points together to get:
You’ll know if you’ve done it right the
two lines cross at the points of
equilibrium that we found earlier: P =
13.33 and Q = 23.33
c) Calculate the price elasticity of demand at equilibrium. (5 marks)
Price elasticity tells us how the consumer responds to a change in price of a good. The question asks
for the price elasticity of demand at equilibrium, so we use the figures for Price and Quantity we
calculated at equilibrium, so P = 13.33 and Q = 23.33 and substitute these into the PED formula:
