Question

2. Cost pass-through in the perfectly competitive market

Consider a perfectly competitive market in which the demand function is q = 100 – 4 p and the supply function is q = - 20 + 2 p.

1. Calculate the market equilibrium price and quantity.
2. Calculate the price elasticity of demand, η, and the price elasticity of supply, ε, at the market equilibrium.
3. Calculate the percentage of pass-through P by using the formulae P = ε/(ε-η).
4. Now, suppose due to government regulation, the supplier would incur an additional cost of $5 for each unit they would supply the market. Show that the supply function now becomes
   q = -30 + 2p.
5. Calculate the new price that the consumers would pay and calculate the increase in the consumer’s price out of the initial increase of $5 per unit. Do we obtain the same number as we did in part c)?

Please Show Work

Answer 1

a)

In equilibrium, quantity demanded=quantity supplied

100-4p=-20+2p

120=6p

p=20

Quantity demanded=100-4*20=20

Quantity supplied=-20+2*20=20

Market equilibrium price=$20

Market equilibrium quantity=20

b)

Demand is given by

Q=100-4P

dQ/dP=-4

Price elasticity of demand is given by

c)

Supply is given by

Q=-20+2P

dQ/dP=2

Price elasticity of demand is given by

d)

Pass through P is given by

d)

In this case, cost is increased by $5 per unit. Seller will get P-5 for each unit will sold.

So, new supply curve is given by

Q=-20+2(P-5)=-20+2P-10=-30+2P

e)

In equilibrium, quantity demanded=quantity supplied

100-4p=-30+2p

130=6p

p=65/3

Increase in consumer price=(65/3-20)=5/3

Increase in consumer price out of initial increase of $5 per unit=(5/3)/5=1/3

Yes, we obtain the same results.