Discussion Week 7 Solutions

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Econ 101: Principles of Microeconomics Fall 2022 Professor Fran Flanagan Week 7 Discussion 1 Content For Today  Trade  Review of Most Missed Exam Questions Questions for Today 1. Consider the market for cars in the United States. Demand is given by D(p) = 60 – p and supply is given by S(p) = 3p. a. Solve for the competitive equilibrium 60-p = 3p ; 60 = 4p ; p = 15, q = 45. b. Suppose the world price for cars (ie the price paid outside of the US) p W = 5. Would the US then import or export cars? Import cars as they are cheaper to buy on the world market than on the domestic market. c. Under free trade, how many cars would the US import/export? Now that US consumers can buy imported cars at p = 5, domestic suppliers must also charge p = 5 or there will be no buyers for their cars. So D(5) = 55 and domestic supply S(5) = 15. 55 – 15 = 40, so the US will import 40 cars at a price of 5 each to cover the domestic shortage at p = 5. d. If the government imposes a tariff of $5/unit what would the domestic price be? If the government imposes a tariff of $5/unit, the world price becomes 10. Given that consumers can buy an imported car for a total price of 10, the domestic producers will match that price, domestic price = 10. e. Under this $5/unit tariff, how many cars would the US import/export? The domestic price is now $10, so D(10) = 50 and S(10) = 30. There is a domestic shortage of 50-30 = 20, so the US will import 20 cars paying $10 for each. Question 6 & 7 Q6) Consumer A values their first apple at $4, their second apple at $3, their third at $2, and their fourth at $1. If the price of apples is p=$1.5/apple, what is A's consumer surplus in equilibrium (assume A can only purchase whole apples; if your answer is not a whole number, enter a decimal, not a fraction). CS = (4-1.5) + (3-1.5) + (2-1.5) = 2.5 + 1.5 + 0.5 = 4.5 Q7) Seller S sells Consumer A the apples. The marginal cost of each apple produced to S is $1.5 (the supply curve is horizontal at p=1.5). Given this, what is S's producer surplus from selling to Consumer A? (If your answer is not a whole number, enter a decimal, not a fraction) Seller S sells 3 apples to Consumer A. For each of these apples they receive p = 1.5 and their cost is 1.5. So for each apple they earn PS = 0.

Econ 101: Principles of Microeconomics Fall 2022 Professor Fran Flanagan Week 7 Discussion 2 Theoretically if we had this market in aggregate with a downward-sloping demand curve and the horizontal supply curve, the graph would look like the one below. Consumer surplus is the triangle below demand and above the price. Producer surplus is the area above the supply curve and below price, in this case supply = 1.5 and price = 1.5 for all quantities so PS = 0. Question 8 & 9 Q8) Market demand is D(p)=100-4p, and supply is S(p)=16p. What is equilibrium quantity q? In equilibrium: 100 – 4p = 16p ; 100 = 20p ; p = 5 and q = 80 Q9) Using the market from the previous question, what is equilibrium Consumer Surplus? (Just enter the number value, not the units) Consider the graph: Demand: P = 25 – ¼Q, Supply: P = 1/16 Q

Econ 101: Principles of Microeconomics Fall 2022 Professor Fran Flanagan Week 7 Discussion 3 CS = ½(20)(80) = (10)(80) = 800 Question 12 In this same market, there will be some deadweight loss after the tax is implemented. Which of the following explanations are reasons why? (Choose all that apply) a) The tax destroys value in the trades that occur b) The tax reduces the consumer surplus from trade that occurs c) The tax reduces producer surplus from the trade that occurs d) There is some welfare increasing trade that occurred in the competitive equilibrium which does not occur under the tax e) The government doesn't use the tax revenue in the market D only. This question has tricky wording. We know there will be deadweight loss after the tax is implemented, as there will be welfare increasing trades that would have occurred in the CE that don’t get to happen post-tax. So we know d is correct. It is very tempting to select a, b, and c too, however those questions refer to trade that still occurs under the tax. Each of the trades that occurs post-tax will create the same amount of surplus that that trade created pre-tax. The loss in surplus is from trades no longer occurring, not from individual trades creating less surplus. Thus a, b, and c are incorrect. E is incorrect because the DWL is unrelated to how tax revenue is used. Question 18

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Econ 101: Principles of Microeconomics Fall 2022 Professor Fran Flanagan Week 7 Discussion 4 Using the same graph from the previous problem, which supply curves intersect the demand curve at a price elastic point? (A point where the price elasticity of demand is elastic; choose all that apply) S_1 and S_2. The demand curve is elastic to the left of its midpoint. The midpoint of this demand curve is at the point where Q = 130/2 = 65. S_1 intersects demand at Q=26, this is to the left of 65. S_2 intersects at Q=52, this is to the left of 65. S_3 intersects at Q=104, this is to the right of 65. So only S_1 and S_2 intersect the demand curve at a price elastic point. Ch5 slides: Question 21

Econ 101: Principles of Microeconomics Fall 2022 Professor Fran Flanagan Week 7 Discussion 5 The graph above represents a market in which the government has imposed a per unit tax of $50/unit sold. After the tax is imposed, what is the deadweight loss? (Just enter the number, not the units.) The competitive equilibrium occurs where S = D, so at the green point where Q = 50 and P = 30. The tax is implemented in purple with the rectangle from P = 20 to 70 and Q = 0 to 10 becoming tax revenue, and the triangle from Q = 10 to 50 becoming deadweight loss. So DWL = (1/2)(40)(50) = (1/2)(2000) = 1000. Ch6 slide: Question 23 Using the same graph, we see that in the competitive equilibrium producers are supplying 50, and after the tax they are supplying 10. Using the graph, and using the midpoint method for elasticity, what is the price elasticity of supply between these two points? Point 1: p1 = 30, S(p1) = 50. Point 2: p2 = 20, S(p2) = 10. Elasticity of Supply = ௌ( ௣ మ ) ିௌ ( ௣ భ ) ௣ మ ି ௣ భ 𝑥 ௣ మ ା ௣ భ ௌ( ௣ మ ) ାௌ( ௣ భ ) = ଵ଴ ିହ଴ ଶ଴ ିଷ 𝑥 ହ଴ ଺଴ = ିସ଴ ିଵ଴ 𝑥 ହ ଺ = 4 ∗ ହ ଺ = ଶ଴ ଺ = ଵ଴ ଷ Question 24

Econ 101: Principles of Microeconomics Fall 2022 Professor Fran Flanagan Week 7 Discussion 6 Fill in the best option from the drop down: Using the same graph, we see that under this tax, consumers are at a price-elastic point on their demand curve. Assuming the tax revenue would change in the same way producer revenue would, we would expect a small reduction in the tax to (increase/decrease/have no effect on) tax revenue. Revenue = PQ and Elasticity of demand = (%change in quantity)/(%change in price). A reduction in the tax will decrease price. At an elastic point on the demand curve, elasticity is less than -1 and so we expect a decrease in the price to be compensated with a larger increase in the quantity demanded. If for example elasticity = -3, if we see the price decrease by 50% we would expect quantity demanded to increase by 150% and total revenue to increase by 25%. Pre-tax decrease: R = PQ Post-tax decrease: R = (0.5P)(2.5Q) = 1.25PQ > PQ.

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