Question

A demand function for milk has been estimated as P = 60 – 3Q and a supply function for milk has been estimated as P = 5 + 2.5Q. 1. Draw a diagram of this market in competitive autarky equilibrium (without the policy). Label all relevant elements (prices, quantities, supply, and demand). Include the numerical values for the important points in your diagram. Calculate consumer surplus, producer surplus, government expenditure, deadweight loss, and total welfare in this market. (7 marks) 2. Modify your diagram to consider the effects of free trade in this market. Assume that the US is a small country, and that the world price of milk is $20 per unit. Label all relevant elements on your diagram (prices, quantities supplied and demanded, imports, supply, and demand). Include the numerical values for the important points in your diagram. Calculate consumer surplus, producer surplus, government expenditure, deadweight loss, and total welfare. You must show your work to receive full marks. (7 marks) 3. Now assume that the US government imposes an import quota of 1.67 units, and that milk farmers are authorised to restrict US milk production (you can assume that milk producers behave as profit- maximising monopolists). Modify your diagram to include the effects of the proposed policy. Label all relevant elements on your diagram (prices, quantities supplied and demanded, imports, supply, and demand). Include the numerical values for the important points in your diagram. Calculate consumer surplus, producer surplus, importer rents, government expenditure, deadweight loss, and total welfare. You must show your work to receive full marks. (16 marks)

Answer 1

The demand and supply functions for milk are: P=60-30 P=5+2.50 1. In the milk market, equilibrium quantity and price are: 60 - 3Q = 5+2.50 5.5Q = 55 Q=10 P=60-3(10) P= 30 The diagram for milk market is shown below: price Demand Supply Initial equilibrium Quantity Consumer surplus (CS) is, CS = 4x(60 – 30)x(10) = 150

Producer surplus (PS) is. PS = x(30–5) x10 = 125 In a competitive equilibrium total surplus is maximum and divided between consumers and producers. So, Government expenditure = 0 Deadweightloss = 0 Total welfare is, Total welfare = CS + PS = 150+125 = 275 2. Suppose world price in the milk market is set at $20. When price is $20, quantity demanded is, P=60-30 20 = 60-30 Q=13.33 And, quantity supplied is, P=5+2.50 20 = 5 +2.50 Q=6 Imports are the gap between quantity demanded and quantity supplied. So. Imports = 13.33-6= 7.33. Following diagram shows the market with world price,

price 60 Demand Supply Initial equilibrium World price 6 10 13.33 Quantity Consumer surplus (CS) is, CS = 5X(60–20)(13.33) = 266.6 Producer surplus (PS) is. PS = 1x(20 – 5) x6 = 45 In a competitive equilibrium total surplus is maximum and divided between consumers and producers. So. Government expenditure = 0 Deadweightloss = 0 Total welfare is,

Total welfare = CS + PS = 266.6+45 = 311.6 3. Suppose import quota of 1.67 units is imposed. The market price for milk will be Qp-Qs =1.67 20- P-2P+2=1.67 P= 27.723 = 10.759 C>= 20-(27.723) = 10.759 Os = {(27.723) - 2 = 9,089 Consider the following diagram of milk market with quota: price 60 Demand Supply Deadweight loss 27.723 Initial equilibrium Price after quota World price PS Government expenditure 6 Quantity 10 13.33 9.089 10.759 Consumer surplus (CS) is. CS = 4x(60 – 27.723)x(10.759) =173.634

Producer surplus (PS) is. PS == x(27.723-5)x9.089 = 103.265 Government expenditure = (10.759–9.089)×(27.723 – 20) = 12.897 Deadweightloss = }}x(27.723–20)x(9.089–6)]+ [3X(27.723–20)(13.33 –10.759) = 11.928 +9.928 = 21.856 Total welfare is, Total welfare = CS + PS + government expenditure =173.634 +103.265 +12.897 = 289.796