PS01__Answers_ - EC 340 Spring 2011 Problem Set 1 The...

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Unformatted text preview: EC 340 Spring 2011 Problem Set 1 The following questions refer to the following diagram that represents the ordinary demand and supply curves for a particular country (call the country “Home” and a particular good (e.g., winter coats). 1. What is the autarky price of winter coats in Home? “Autarky” means a situation of self‐sufficiency, where the country neither imports nor exports the product. In this example, the quantity of coats demanded equals the quantity supplied when the price of coats is $100. This is then the autarky price. 2. Suppose that Home is an importer of winter coats. Draw the import demand curve. The import demand curve shows the quantity of imports that Home would demand at each price. In general quantity of imports demanded = (quantity of coats demanded – quantity of coats supplied). Quantity of Coats Quantity of Coats Quantity of Imports Price Demanded Supplied Demanded 100 140 140 0 75 165 90 75 50 190 40 150 25 215 0 215 Note that there is a “kink” in this import demand curve because the quantity supplied is zero below a price of $25, even though the quantity demanded is still positive. P 100 SX 75 50 25 DM 10 75 150 215 Q 3. Suppose that the autarky price of winter coats in the other country (call it “Foreign”) is 10 and that the equilibrium price with trade is 50. Draw the export supply curve (in the same graph that you drew to answer question 2) that is consistent with this information.’ The intercept of the export supply curve corresponds to the autarky price in Foreign. Since the equilibrium price with trade is $50, the quantity of exports supplied must equal the quantity of imports demanded (in this case, the quantity is 150). So these are two points on the export supply curve (when price is $10, the quantity of exports is zero, when price is $50, the quantity of exports supplied is 150). 4. Based on the information so far, what does trade imply for producer surplus in Home? Be specific, describing both the direction of change (if any) and its size. Trade causes price in Home to fall. This harms producers. The loss of producer surplus is represented by the shaded region in the following diagram. This area of this trapezoid can be can be calculated either as the sum of the area of a rectangle and a triangle, OR as ½*height*(short base + long base). Using the second formula, we have ½*($100 ‐ $50)*(40 + 140) = $4,500. This is a loss. 5. Based on the information so far, what does trade imply for consumer surplus in Home? Be specific, describing both the direction of change (if any) and its size. Trade causes price in Home to fall. This benefits consumers. The gain in consumer surplus is represented by the shaded region in the following diagram. This area of this trapezoid can be can be calculated either as the sum of the area of a rectangle and a triangle, OR as ½*height*(short base + long base). Using the second formula, we have ½*$50*(140 + 190) = $8,250. 6. What is the net welfare effect of trade on Home? The net welfare effect equals the gain to the consumer minus the loss to the producer: $8,250 ‐ $4,500 = $3,750 This is also the area of the shaded triangle in the following figure: To double‐check the answer, calculate the area of the triangle ½ * base * height = ½*$50*150 = $3,750 7. What is the net welfare effect of trade on Foreign? We don’t have the ordinary demand and supply for the exporting country, but we can derive the net welfare effect from the import demand and export supply diagram. As described in class, the net welfare effect is positive, and it equals the ½*(free trade price – autarky price)*quantity of exports. In this example: ½*($50 ‐ $10)*150 = $3,000. This is also the area of the shaded triangle in the following diagram: P 100 SX 75 50 25 DM 10 75 150 215 Q ...
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