Final answer:
To calculate the gain in consumer surplus when transitioning from autarky to free trade, we find the area of the triangle defined by the difference in quantities and the price change between autarky and the world price.
Step-by-step explanation:
The student's question involves calculating the change in domestic consumer surplus when moving from autarky to free trade in a small open economy model. In such a model, the domestic consumer surplus can be graphically represented by the area under the demand curve and above the equilibrium price. Under autarky, the equilibrium is where domestic quantity demanded equals domestic quantity supplied. With free trade, the economy takes the world price as given. If we assume the world price is $24, to determine the consumer surplus, we first find the quantity demanded at this price using the given domestic demand equation QD = 120 - 2p. Substituting p with 24, we get QD = 120 - 2(24) which results in QD = 72. The domestic supply at that price can be found by the equation Qs = 1/2 p, and substituting p with 24 gives us Qs = 1/2(24), which results in Qs = 12.
The difference between QD and Qs, which is 60 (72 - 12), represents the quantity of imports at the world price. To calculate the gain in consumer surplus due to moving to free trade, we find the area of the triangle with base equal to the quantity difference (60) and the height equal to the difference between the original autarky price and the world price. To find the autarky price, we set QD equal to Qs, so 120 - 2p = 1/2 p, solving for p gives us the autarky price. The consumer surplus gained is then (1/2 * base * height), with the base being the difference in quantity (60) and the height being the difference between autarky and world prices.