Question

Suppose the US domestic demand for bicycles can be described as the following demand function: Q^D=25000-150P. The supply function of bicycles is assumed to be Q^S=15000+50P.

1. We assume that the bicycle market is competitive. What is the equilibrium price and its equilibrium quantity?

2. Calculate the consumer surplus, producer surplus, and the total surplus.

3. Suppose that due to a trade agreement, the US bicycle market now welcomes foreign bicycles and starts importing bicycles from other countries. The world market is competitive, and its price is at $40, i.e. each imported bicycle will cost a US consumer $40 and the supply of imported bicycles is sufficiently large. The trade agreement impacted the market and it has moved to a new equilibrium. What is the new equilibrium price for the US market?

4. At the new equilibrium, what is the quantity demanded for bicycles now? How many bicycles will domestic producers produce? And how many bicycles are from imports?

5. What is the total surplus in this market now? Compare your answer to the total surplus calculated in part 2. What is the net gain in social welfare?

6. Has the U.S. as a whole benefited by opening up trade to the rest of the world? If it has not, explain why. If it has, does it imply that EVERYONE wins in this event? Who might have losses?

Answer 1

Suppose the US domestic demand for bicycles can be described as the following demand function: Q^D=25000-150P. The supply function of bicycles is assumed to be Q^S=15000+50P.

1. The bicycle market is competitive. Equilibrium price and equilibrium quantity are found at

Qd = Qs

25000 – 150P = 15000 + 50P

10000 = 200P

P = 50 and Q = 15000 + 50*50 = 17500 units

2. Consumer surplus = 0.5*(max price – price paid)*quantity purchased = 0.5*(166.67 – 50)*17500 = 1020863, Producer surplus = 0.5*(50 – 0)*(17500 + 15000) = 812500, and the total surplus = PS + CS = 1833363.

3. The world market is competitive at a price = $40. The new equilibrium price for the US market is $40 because domestic price is greater than $40 and consumers will prefer to buy from foreign sellers at $40.

4. At the new equilibrium, the quantity demanded for bicycles now is 19000 units. Domestic production is reduced to 17000 units so imports are 2000 units

5. Total surplus in this market now is CS + PS = 0.5*(166.67 – 40)*19000 + 0.5*(40 – 0)*(17000 + 15000) = 1843365. Total surplus is now increased and so the net gain in social welfare is 10002.

6. U.S. as a whole benefited by opening up trade to the rest of the world. Buyers have gained 1203365 – 1020863 = 182502 while producers have lost 812500 – 640000 = 172500. In total there is a net gain of 182502 – 172500 = 10002.