Home Work 6 - Fall - 2023 - Answer Key

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Econ 3HH3 Fall 2023 Home Assignment #6: Answer Key 1. (2 points) Consider two demand functions that describe the relationship between the price of a cup of coffee, and the quantity of cups, Q. Which demand is more elastic? Explain why. P = 100 – 5Q P = 300 – 6Q Answer: The second demand function is less elastic, since it is steeper than the first one, so that if the price is reduced (or increased) by $1, in the second case the change in the quantity demanded will be smaller. 2. (2 points) Based on the IIT index, which sector from the table below has the highest share of intra-industry trade? Exports Imports Sector A $3,000 $12,000 Sector B $25,000 $15,000 Sector C $11,000 $14,000 Answer: Index of IIT = (Min of Imports and Exports) / [1/2* (Imports + Exports)] IIT Index Sector A 0.4 Sector B 0.75 Sector C 0.88 So Sector C has the highest shares. 3. (4 points) Based on the information below about the production structure, explain whether the technology used in each part demonstrates constant returns to scale (CRS) or increasing returns to scale (IRS) property. a. The labor cost of production of Q units of a good is given by C(Q) = 12Q b. The marginal labor cost of production of Q units of a good is 8 , while the fixed cost of producing Q units is 20. c. To produce a good, one needs to use capital K and labor L. The quantity Q produced using L units of labor and K units of capital is given by Q = 38(L) 0.4 (4K) 0.6 d. To produce a good, one needs to use capital K, labor L, and electricity E. The quantity Q produced using L units of labor, K units of capital, E units of electricity, and C units of coal is given by Q = 25(3L) 0.2 (9K) 0.4 (0.4E) 0.3 (0.6C) 0.2 Answer: IRS means increasing average costs of production, while CRS means constant average costs. Thus, we need to look at AC(Q) = C(Q)/Q. In part (a) AC(Q) = 12, so this is CRS technology. In part (b) C(Q) = 8Q + 20 so that AC(Q) = 8 + 20/Q, so this is IRS technology. The alternative definition of CRS and IRS is related to the change in inputs and the resulting

change in the output. If all inputs are increased by some proportion, then if the output rises by the same proportion, then we have CRS technology, and if the output rises faster than this proportion, we have IRS technology. For simplicity, let us see what happens with the output, if all inputs are doubled. In part (c), Q old (L,K) = 3(L) 0.4 (4K) 0.6 , Q new (2L,2K) = 3(2L) 0.4 (4*2K) 0.6 = 2Q old (L,K) Hence, the output is doubled, i. e., we have CRS technology. In part (d), Q old (L,K) = 25(3L) 0.2 (9K) 0.4 (0.4E) 0.3 (0.6C) 0.2 , Q new (2L,2K) = 25(3*2L) 0.2 (9*2K) 0.4 (0.4*2E) 0.3 (0.6*2C) 0.2 = 2 1.1 Q old (L,K) Hence, the output is more than doubled, i. e., we have IRS technology. 4. (2 points) Of three products, milk, meat, and cheese, which do you expect to have a higher index of intra-industry trade? Why? Answer: We would expect that cheese would have a higher index of industry trade, because there are many more differentiated varieties of cheese traded by many countries than milk or meat. So consumers in many countries do buy a lot of different varieties of cheese that are imported. That being said, it is important that the product is not only imported but is exported as well. IIT index for cheese can be high only if the country that imports cheese exports it as well. If this is not the case, then IIT index for cheese could be low. Similar considerations can be given to meat and milk: there are smaller numbers of varieties of these products than of cheese but some countries can export and import large quantities of both meat and milk. Let’s look at Canada as an example. Canadian cheese is exported in large quantities as well as milk and meat. So the answer to the question about IIT strongly depends on the actual numbers. If we consider 2018, for example, the IIT index is the highest for meat: Meat: http://www.agr.gc.ca/eng/industry-markets-and-trade/canadian-agri-food-sector- intelligence/red-meat-and-livestock/red-meat-and-livestock-market-information/trade- balance/?id=1415860000005 Cheese and Milk: http://www.dairyinfo.gc.ca/index_e.php?s1=dff-fcil&s2=imp-exp&s3=exp

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