Question

Questions: Consider a small open economy of Jamaica whose domestic supply and demand of rum is as follows.

Demand: Q = 500 - P

Supply: Q = 2:5P - 25

where quantity is in thousands of crates and price is in Jamaican dollars (J$).

i) What are the equilibrium price and quantity in autarky equilibrium? (5 points)

ii) Now suppose the world price of rum is J$ 100. In an attempt to protect local rum

producers, the government imposes a quota of 105 thousand crates on imports of

rum.

a) What will be the local price of a crate of rum, given the quota?

b) What is the value of the consumption deadweight cost associated with the quota?

iii) When the demand for rum changes to Q = 447:5 ? P, will the deadweight cost

decrease or increase?

Hint: You do not need to calculate the actual value of the deadweight cost

Answer 1

Demand: Q = 500 - P

Supply: Q = 2.5P - 25

At equilibrium,

2.5P - 25 = 500 - P

or 3.5 P = 525

or P = 150

Q = 500 - 150 = 350

So under autarly the equilibrium quantity will be 350 and the equilibrium price will be 150.

If there is a quota of 105 thousand crates,

Demand - Supply = 105

or 500 - P - (2.5P - 25) = 105

or 525 - 3.5P = 105

or 3.5P = 420

or P = 120

So the equilibrium price will be 120 after imposition of the quota.

Quantity Demanded = 500- 120 = 380

Price without quota = 100

Quantity demanded without quota = 500 - 100 = 400

Consumer Deadweight Loss = Change in Quantity * Change in Price / 2 = (400 - 380) * (120 - 100) / 2= 200

iii) If the demand is Q = 447.5 - P, it means that the quantity demanded is lesser. This means that the deadweight cost will decrease since the demand curve shifts downwards. So the change in quantity demanded is lower as is the change in price which leads to a lower deadweight cost.

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