Question

The demand and supply for a good are respectively QD = 16 – 2P + 2I and QS = 2P – 4 with QD denoting the quantity demanded, QS the quantity supplied, and P the price for the good. Suppose the consumers’ income is I = 2.

i) Determine producers’ total cost (there are no fixed costs) at the equilibrium. ii)Determine the producer surplus at the equilibrium. iii)) Determine the total surplus at the equilibrium..

Answer 1

Demand function: QD = 16-2P +2I

Put I = 2

=> QD = 16 -2P + 2(2)

=> QD = 16 - 2P +4

=> QD = 20 - 2P

and

QS = 2P -4

At equilibrium point; QD = QS

=> 20 -2P = 2P -4

=> 20 +4 = 2P +2P

=> 24 = 4P

=> P = 24 / 4

=> P = 6

Hence, equilibrium price is 6

and

QD = QS = Q (At equilibrium)

=> Q = 2P - 4

=> Q = 2(6) - 4

=> Q = 12 -4

=> Q = 8

Hence, equilibrium quantity is 8

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Equilibrium occurs at point B

Variable cost is the area of region BDOE

Area of region BEOC = (BE) (EO)

=> Area of region BEOC = (6 -0) (8-0)

=> Area of region BEOC = 6 * 8

=> Area of region BEOC = 48

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Area of region BCD = 0.5 (BC) (CD)

=> Area of region BCD = 0.5 (8-0) (6-2)

=> Area of region BCD = 0.5 (8) (4)

=> Area of region BCD = 16

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Area of region BDOE = Area of region BEOC - Area of region BCD

=> Ares of region BDOE = 48 -16

=> Area of region BDOE = 32

Hence, the variable cost is 32

and there is no fixed cost

Total cost = fixed cost + variable cost

=> Total cost = 0 + 32

=> Total cost = 32

Answer: The total cost at equilibrium is 32

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(b)

Producer surplus at equilibrium = Area of region BCD

=> Producer surplus at equilibrium = 0.5 (BC) (CD)

=> Producer surplus at equilibrium = 0.5 (8-0) (6-2)

=> Producer surplus at equilibrium = 0.5 (8) (4)

=> Producer surplus at equilibrium = 16

Answer: Producer surplus at equilibrium is 16

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(c) Consumer surplus at equilibrium = Area of region ABC

=> Consumer surplus at equilibrium = 0.5 (AC) (BC)

=> Consumer surplus at equilibrium = 0.5 (10-6) (8-0)

=> Consumer surplus at equilibrium = 0.5 * 4 * 8

=> Consumer surplus at equilibrium = 16

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Total surplus = consumer surplus + producer surplus

=> Total surplus = 16 + 16

=> Total surplus = 32

Answer: Total surplus at equilibrium is 32