Question

Q1: The market for iron is represented by Q = 2P – 30 and Q = 360 – 3P and where Q is the quantity of iron measured in tonnes and P is the price of iron measured in dollars per tonne.

a) What are the equilibrium price and equilibrium quantity in this market?

b) What does the demand value (V_D) of the 60^th tonne of iron equal?

c) What does the supply value (V_S) of the 60^th tonne of iron equal?

d) What does consumer surplus of the 60^th tonne of iron equal?

e) What does producer surplus of the 60^th tonne of iron equal?

f) What does consumer surplus of the first 60 tonnes of iron equal? Show your calculations. Hints: There is a difference between this question and question d). Draw a demand and supply graph. This question involves lots of calculations.

g) What does producer surplus of the first 60 tonnes of iron equal? Show your calculations. Hints: There is a difference between this question and question e). Draw a demand and supply graph. This question involves lots of calculations.

Answer 1

a) At equilibrium, demand = supply

2P - 30 = 360 - 3P

P = 78

At this price, Q = 126

b) Demand value of 60th ton equal: 60 = 2P - 30

P = 45

c) Supply value of 60th ton equal: 60 = 360 - 3P

P = 100

d) Consumer surplus of 60th ton equal the maximum price they are willing to pay - price they are paying for 60th unit = 120 - 100 = 20

e) Producer surplus of 60th ton equal the price they are receiving for 60th unit - minimum price they are willing to receive = 45 - 15 = 30

f) Total consumer surplus of 60 units is area of portion A in the above diagram whose sum is(1/2) * (120 - 100) * (60 - 0) = 600

g) Total producer surplus of 60 units is area of portion B in the above diagram whose sum is (1/2) * (45 - 15) * (60 - 0) = 900