Office Hours: Monday 3:00-4:00 – LUMS C85 ECON 101 Tutorial: Week 11 Shane Murphy s.murphy5@lancaster.ac.uk Office Hours: Monday 3:00-4:00 – LUMS C85

Outline Roll Call Problems Summary

𝑂𝑝𝑝𝑜𝑟𝑡𝑢𝑛𝑖𝑡𝑦 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑔𝑜𝑜𝑑 𝑦= 𝑆𝑎𝑐𝑟𝑖𝑓𝑖𝑐𝑒 𝑜𝑓 𝑔𝑜𝑜𝑑 𝑥 𝐺𝑎𝑖𝑛 𝑖𝑛 𝑔𝑜𝑜𝑑 𝑦 Question 2(a) The table below shows the production possibilities for two products, pens and pencils. Calculate the opportunity cost of producing 1 additional pen between points A and B. The opportunity cost of pens between A and B is one pen for two pencils. OP = (10-0)/(10-5) = 2 In general, the equation to calculate opportunity cost is: 𝑂𝑝𝑝𝑜𝑟𝑡𝑢𝑛𝑖𝑡𝑦 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑔𝑜𝑜𝑑 𝑦= 𝑆𝑎𝑐𝑟𝑖𝑓𝑖𝑐𝑒 𝑜𝑓 𝑔𝑜𝑜𝑑 𝑥 𝐺𝑎𝑖𝑛 𝑖𝑛 𝑔𝑜𝑜𝑑 𝑦 Point Pens Pencils A 10 B 5 C 2 25

Question 2(b) The table below shows the production possibilities for two products, pens and pencils. Calculate the opportunity cost of producing 1 additional pencil between points A and B. The opportunity cost of pencils between A and B is one pencil for half a pen. OP = (10-5)/(10-0) = ½ Point Pens Pencils A 10 B 5 C 2 25

Question 2(c) The table below shows the production possibilities for two product, pens and pencils. Calculate the opportunity cost of producing 1 additional pen between points B and C. What conclusions can you come to about this opportunity cost compared to the calculation you made in part(a)? The opportunity cost of pens between B and C is one pen for five pencils. OP = (25-10)/(5-2)) = 5 This is a much higher opportunity cost than between A and B. Point Pens Pencils A 10 B 5 C 2 25

Question 2(d) The table below shows the production possibilities for two products, pens and pencils. Calculate the opportunity cost of producing 1 additional pencil between points B and C. What conclusions can you come to about this opportunity cost compared to the calculation you made in part (b)? The opportunity cost of pencils between B and C is one pencil for 1/5 of a pen. OP = (5-2)/(25-10) = 1/5 This is a much lower opportunity cost than between A and B. Point Pens Pencils A 10 B 5 C 2 25

Number of Workers needed to make: Number of Workers needed to make: Question 3(a) Swedish and Danish workers can each produce 4 cars a year. A Swedish worker can produce 10 tonnes of grain a year, whereas a Danish worker can produce 5 tonnes of grain a year. Assume that each country has 100 million workers. Construct a table showing the production opportunities of both countries. First thing to do is use the information above to find out how many workers are needed to produce one car and one ton of grain per year:   Number of Workers needed to make: One car per year One tonne of grain per year Swedish ¼ 1/10 Danish 1/5   Number of Workers needed to make: One car per year One tonne of grain per year Swedish Danish

Question 3(a) ctd. In the prev. slide, we found how many workers are needed to produce one unit of each good. Now we want to show how much each country will produce in a year. We assume each country has 100 million workers. So, we divide the total number of workers by the number of workers needed to produce one unit of each good per year: Note: You might not always have a problem that looks at amount produced by a certain number of workers. See Slide 14 in Week 10 Lecture Slides for an example that looks at the amount produced in a certain amount of time.   Number of Workers needed to make: Amount produced in a year by 100 million workers One car per year One tonne of grain per year Cars Tonnes of grain Swedish ¼ 1/10 400 million 1,000 million Danish 1/5 500 million   Number of Workers needed to make: Amount produced in a year by 100 million workers One car per year One tonne of grain per year Cars Tonnes of grain Swedish ¼ 1/10 Danish 1/5

Amount produced in a year by 100 million workers Question 3(b) Graph the production possibilities frontier of the Swedish and Danish economies. So, here is what we will be graphing: I’ve put cars on the Y-axis and grain on the X-axis:   Amount produced in a year by 100 million workers Cars Tonnes of grain Swedish 400 million 1,000 million Danish 500 million 500 1000 Grain Cars   400 Swedish Danish Y-axis: With 100 million workers and four cars per worker, if either economy were devoted completely to cars, it could make 400 million cars. X-axis: Since a Swedish worker can produce 10 tonnes of grain, if Sweden produced only grain it would produce 1,000 million tonnes. Since a Danish worker can produce 5 tonnes of grain, if Denmark produced only grain it would produce 500 million tonnes. Note: Because the trade-off between cars and grain is constant, the production possibilities frontier is a straight line. Some notes on the PPF (from the Week 10 Lecture Slides): The production possibilities frontier (PPF) is a graph that shows the combinations of output that the economy can possibly produce given the available factors of production and the available production technology Production is efficient at points on the curve Production is inefficient inside the curve Production at a point outside of the curve is not possible given the economy’s current level of resources and technology

Amount produced in a year by 100 million workers Question 3(c) For Sweden, what is the opportunity cost of a car? Of grain? For Denmark, what is the opportunity cost of a car? Of grain? Put this information in a table. We’ll use the information that we found in part (b): And we’ll use our equation for Opportunity Cost: 𝑂𝑝𝑝𝑜𝑟𝑡𝑢𝑛𝑖𝑡𝑦 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑔𝑜𝑜𝑑 𝑦= 𝑆𝑎𝑐𝑟𝑖𝑓𝑖𝑐𝑒 𝑜𝑓 𝑔𝑜𝑜𝑑 𝑥 𝐺𝑎𝑖𝑛 𝑖𝑛 𝑔𝑜𝑜𝑑 𝑦   Amount produced in a year by 100 million workers Cars Tonnes of grain Swedish 400 million 1,000 million Danish 500 million   Opportunity cost of 1 car (in terms of grain given up) 1 tonne of grain (in terms of cars given up) Sweden 2.5 0.4 Denmark 1.25 0.8   Opportunity cost of 1 car (in terms of grain given up) 1 tonne of grain (in terms of cars given up) Sweden Denmark

Amount produced in a year by 100 million workers Question 3(d) Which country has an absolute advantage in producing cars? In producing grain? First, let’s define Absolute advantage: Someone has absolute advantage if they can produce more output than others, using the same amount of inputs. Or, we could say that they produce the same output as others, using fewer inputs. So, what we want to compare is the output per worker between the two countries: Neither country has an absolute advantage in producing cars, because they are equally productive (same output per worker). Sweden has an absolute advantage in producing grain, because it is more productive (greater output per worker).   Amount produced in a year by 100 million workers Cars Tonnes of grain Swedish 400 million 1,000 million Danish 500 million If you’d like another example of absolute advantage and comparative advantage, here is a brief video: https://www.khanacademy.org/economics-finance-domain/microeconomics/choices-opp-cost-tutorial/gains-from-trade-tutorial/v/comparative-advantage-and-absolute-advantage

Question 2(e) Which country has a comparative advantage in producing cars? In producing grain? First, let’s define Comparative advantage: One person has a comparative advantage over another in a task if his or her opportunity cost of performing a task is lower than the other person’s opportunity cost. So, we’ll use the opportunity cost that we found in part (c): Denmark has a comparative advantage in producing cars, because it has a lower opportunity cost in terms of grain given up. Sweden has a comparative advantage in producing grain, because it has a lower opportunity cost in terms of cars given up.   Opportunity cost of 1 car (in terms of grain given up) 1 tonne of grain (in terms of cars given up) Sweden 2.5 0.4 Denmark 1.25 0.8

Question 3(f) Without trade, half of each country’s workers produce cars and half produce grain. What quantities of cars and grain does each country produce? So, 50 million workers will produce cars and the other 50 million will produce grain in each country. We know that: Sweden would produce 200 million cars (50 million workers times 4 cars each), and 500 million tonnes of grain (50 million workers times 10 tonnes each). Denmark would produce 200 million cars (50 million workers times 4 cars each) and 250 million tonnes of grain (50 million workers times 5 tonnes each).   Number of Workers needed to make: Amount produced in a year by 1 worker One car per year One tonne of grain per year Cars Tonnes of grain Swedish ¼ 1/10 4 10 tonnes Danish 1/5 5 tonnes

Question 3(g) Starting from a position without trade, give an example in which trade makes each country better off. From any situation with no trade, in which each country is producing some cars and some grain, suppose Sweden changed 1 worker from producing cars to producing grain. That worker would produce 4 fewer cars and 10 additional tonnes of grain. Then suppose Sweden offers to trade 7 tonnes of grain to Denmark for 4 cars. Sweden will do this because it values 4 cars at 10 tonnes of grain, so it will be better off if the trade goes through. Suppose Denmark changes 1 worker from producing grain to producing cars. That worker would produce 4 more cars and 5 fewer tonnes of grain. Denmark will take the trade because it values 4 cars at 5 tonnes of grain, so it will be better off. With the trade and the change of 1 worker in both Sweden and Denmark, each country gets the same amount of cars as before, and both get additional tonnes of grain (3 for Sweden and 2 for Denmark). Thus by trading and changing their production, both countries are better off.

Question 4(a) Morgan and Oliver share a flat. Their favourite activities are cooking pizza and making homebrew beer. Oliver takes 4 hours to produce 1 barrel of beer, and 2 hours to make a pizza. Morgan takes 6 hours to produce 1 barrel of beer, and 4 hours to make a pizza. What is each flatmate’s opportunity cost of making a pizza? Oliver’s opportunity cost of making a pizza = ½ barrel of beer because he could brew ½ barrel in the time (2 hours) it takes him to make a pizza. Morgan’s opportunity cost of making a pizza = 2/3 barrels of beer because she could brew 2/3 of a barrel in the time (4 hours) it takes her to make a pizza. Who has the absolute advantage in making pizza? Oliver has an absolute advantage in making pizza since he can make one in two hours, while it takes Morgan four hours. (In other words, he uses fewer inputs (time, in this case) than Morgan to produce the same amount of output as Morgan) Who has the comparative advantage in making pizza? Oliver has a comparative advantage in making pizza because Oliver’s opportunity cost of making pizza is less than Morgan’s.

Question 4(b) If Oliver and Morgan trade foods with each other, who will trade away pizza in exchange for beer? Since Oliver has a comparative advantage in making pizza, he will make pizza and exchange it for beer that Morgan makes. Note: This is an example of the principle of comparative advantage. It states that under free trade, the individual will produce more of and consume less of a good for which he has a comparative advantage.

Question 4(c) The price of pizza can be expressed in terms of barrels of beer. What is the highest price at which pizza can be traded that would make both flatmates better off? What is the lowest price? Explain. The highest price of pizza in terms of beer that will make both flat-mates better off is 2/3 of a barrel of beer. If the price were higher than that, then Morgan would prefer making her own pizza (at an opportunity cost of 2/3 of a barrel of beer), rather than trading for pizza that Oliver makes. The lowest price of pizza in terms of beer that will make both flat-makes better off is ½ of a barrel of beer. If the price were lower than that, then Oliver would prefer making his own beer (he can make ½ a barrel of beer instead of making a pizza) rather than trading for beer that Morgan makes. In short: The highest price of pizza where both will be better off = the buyer’s opportunity cost of pizza The lowest price of pizza where both will be better off = the seller’s opportunity cost of pizza So, the feasible price range lies between the opportunity cost of the two flat-mates.

Bonus Question Consider a small country that imports bananas at the price of £20 per bag. The demand curve is D = 500 – 5P. The supply curve is S = -50 + 5P. Determine the no-trade equilibrium. What is consumer surplus and producer surplus? For the no-trade equilibrium, we set demand equal to supply: 500−5𝑃=−50+5𝑃 Solving, we find 𝑃=55. We can then substitute into demand (or supply) to get Q 𝑄=500−5 55 =225. If we graph our Supply and Demand curves, we should get: To find consumer and produce surplus: 𝐶𝑆= 1 2 100−55 225 𝐶𝑆=5062.50 𝑃𝑆= 1 2 55−10 225 𝑃𝑆=5062.50

Bonus Question Determine the free trade equilibrium. What is consumer surplus and producer surplus? If we impose the free trade price of £20, we can substitute that into the demand curve to get 𝐷=400, and substituting into the supply curve gives 𝑆=50. Graphically, we have: So consumer surplus is 𝐶𝑆= 1 2 100−20 400 =16,000, and producer surplus is 𝑃𝑆= 1 2 20−10 50 =250. Note there are gains from trade: with trade, 𝑃𝑆+𝐶𝑆=16,250, which compares with the no trade scenario in part (a) 𝑃𝑆+𝐶𝑆=10,125. This question is coming straight from the examples in Week 10 Lecture Slides 28-38.

Bonus Question Suppose the country now imposes an import tariff of £10 per bag of bananas. Draw the diagram for this policy. Solve for equilibrium prices and quantities of the equilibrium with the tariff. Calculate the effects on consumer surplus, producer surplus, government revenue, and the net welfare effect of the tariff. Imposing an import tariff of £10 per bag raises the world price to £30. We can substitute this into the demand and supply curves curve to get 𝐷=350 and 𝑆=100. Graphically, we would have: Now, consumer surplus is 𝐶𝑆= 1 2 100−30 350 =12250, And producer surplus is 𝑃𝑆= 1 2 30−10 100 =1000. Tariff revenue is 𝑇𝑅=10× 350−100 =2,500. Hence the net welfare effect of the tariff (compared to free trade) is Δ𝐶𝑆+Δ𝑃𝑆+𝑇𝑅= 12,250−16,000 + 1,000−250 +2,500= −500 That is, there is a net welfare loss of imposing the import tariff. However, producers win while consumers lose. Parts C and D are coming from examples in Week 10 Lecture Slides 39-53.

Bonus Question Suppose now that (without the tariff) the country imposes a quota that limits imports to 50 bags. Solve for equilibrium prices and quantities of the equilibrium with the quota. Calculate the effects on consumer surplus, producer surplus, and the quota rent. Now, if instead of a tariff, an import quota is imposed instead, what this does is to shift the supply curve to the right (this now becomes a supply curve which combines both domestic and imported goods). Mathematically, the supply curve is now: 𝑆=−50+5𝑃+50=5𝑃. Now, setting this equal to demand gives: 5𝑃=500−5𝑃 Hence 𝑃=50, and substituting into the demand curve (or the new supply curve) gives 𝑄=250. This is the total quantity demanded, of which 50 units is imported, so domestic supply is 200. Hence consumer surplus is 𝐶𝑆= 1 2 100−50 250 =6250, and producer surplus is 𝑃𝑆= 1 2 50−10 200 =4000. Hence the change in consumer surplus is Δ𝐶𝑆=6250−16000=−9750, and the change in producer surplus is Δ𝑃𝑆=4000−250=3750.   The quota rent is 250−200 50−20 =1,500. Parts C and D are coming from examples in Week 10 Lecture Slides 39-53.

The effects of an import quota

The effects of an import quota

Summary The Production Possibilities Frontier provides a model to show potential output of goods and services in an economy and the opportunity cost ratios of diverting resources to different uses There are two ways to compare the ability of two people producing a good: The person who can produce a good with a smaller quantity of inputs has an absolute advantage The person with a smaller opportunity cost has a comparative advantage The gains from trade are based on comparative advantage, not absolute advantage

Summary Trade makes everyone better off because it allows people to specialise in those activities in which they have a comparative advantage When a country allows trade and becomes an exporter of a good, producers of the good are better off, and consumers of the good are worse off When a country allows trade and becomes an importer of a good, consumers of the good are better off, and producers are worse off

Summary The effects of free trade can be determined by comparing the domestic price without trade to the world price: A low domestic price indicates that the country has a comparative advantage in producing the good and that the country will become an exporter A high domestic price indicates that the rest of the world has a comparative advantage in producing the good and that the country will become an importer A tariff – a tax on imports – moves a market closer to the equilibrium that would exist without trade, and therefore reduces the gains from trade Import quotas will have effects similar to those of tariffs

Next Class Week 12 Worksheet Short-Answer Exam is Next Friday!

Math Questions For the following questions, solve for 𝑑 2 𝑦 𝑑 𝑥 2 . 1. 𝑦=−35 − 𝑥 2 + 4 3 𝑥 −3 2. 𝑑𝑦 𝑑𝑥 =39 −2 𝑒 0.5𝑥 + 𝑥 2 −3𝑥 3. 𝑦=5 log 𝑒 𝑥+ 𝑒 5𝑥 +5 𝑥 5 4. 𝑦=−8 𝑒 −0.5𝑥 −4 𝑒 0.5𝑥 −3 log 𝑒 𝑥+ 3 4 𝑥 2 −2 𝑥 −3 5. 𝑑𝑦 𝑑𝑥 =− 4 5 𝑥 1 2 +12 log 𝑒 𝑥 + 4 5 𝑒 0.25𝑥

Math Solutions For the following questions, solve for 𝑑 2 𝑦 𝑑 𝑥 2 . 𝑦=−35 − 𝑥 2 + 4 3 𝑥 −3 𝑑𝑦 𝑑𝑥 =−2𝑥 −4 𝑥 −4 → 𝑑 2 𝑦 𝑑 𝑥 2 =−2+16 𝑥 −5 2. 𝑑𝑦 𝑑𝑥 =39 −2 𝑒 0.5𝑥 + 𝑥 2 −3𝑥 𝑑 2 𝑦 𝑑 𝑥 2 = −𝑒 0.5𝑥 +2𝑥 −3 3. 𝑦=5 log 𝑒 𝑥+ 𝑒 5𝑥 +5 𝑥 5 𝑑𝑦 𝑑𝑥 = 5 𝑥 +5 𝑒 5𝑥 +25 𝑥 4 → 𝑑 2 𝑦 𝑑 𝑥 2 =−5 𝑥 −2 +25 𝑒 5𝑥 +100 𝑥 3 4. 𝑦=−8 𝑒 −0.5𝑥 −4 𝑒 0.5𝑥 −3 log 𝑒 𝑥+ 3 4 𝑥 2 −2 𝑥 −3 𝑑𝑦 𝑑𝑥 =4 𝑒 −0.5𝑥 −2 𝑒 0.5𝑥 − 3 𝑥 + 3 2 𝑥+6 𝑥 −4 → 𝑑 2 𝑦 𝑑 𝑥 2 =−2 𝑒 −0.5𝑥 − 𝑒 0.5𝑥 +3 𝑥 −2 + 3 2 −24 𝑥 −5 5. 𝑑𝑦 𝑑𝑥 =− 4 5 𝑥 1 2 +12 log 𝑒 𝑥 + 4 5 𝑒 0.25𝑥 𝑑 2 𝑦 𝑑 𝑥 2 =− 2 5 𝑥 − 1 2 + 12 𝑥 + 1 5 𝑒 1 4 𝑥 or you could write 𝑑 2 𝑦 𝑑 𝑥 2 =− 2 5 𝑥 −0.5 +12 𝑥 −1 + 1 5 𝑒 0.25𝑥