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101hw5 - Department of Agricultural and Resource Economics...

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Department of Agricultural and Resource Economics EEP101/ECON125 University of California, Berkeley David Zilberman Solutions to Problem set 5 1. Climate change, see Chapter 14, pp1-2. Which crop to produce is determined by the relative profitability of the two crops in that particular location. In general, the profit functions as of L are: π H = [5(5 – L) – (5 – L) 2 )*C, π C = [5(8 – L) – (8 – L) 2 )*C. We could solve for L* where π H = π C , then we could identify the regions where corn will be produced and the regions where wheat will be produced. Alternatively, we could solve for the profits for both crops for each location, and then conclude the production pattern. a. Before climate change, T = 8 – L, C = 1, so π H = π C Î [5(5 – L) – (5 – L) 2 ) – [5(8 – L) – (8 – L) 2 )= 0. Solve and yield L* = 4. The production pattern and profit distribution are summarized in the table below. b. After climate change, T = 10 – L, and C = 1.1. The change suggested that the temperature in all locations is higher, i.e. there exists global warming. We follow the same approach used in part a, π H = [5(7 – L) – (7 – L) 2 )*1.1 = π C = [5(10 – L) – (10 – L) 2 )*1.1, Î L* = 6. The production allocation and profit distribution are summarized in the table below. Locations 0 and 1 withdraw production while locations 9 and 10 join in the production. Locations 4, 5, 6 switch from wheat to corn. Farmers ion locations 1,2,3, and 6 lose while farmer in locations 4, 5, 7, 8, and 9 gain. As a whole, the society would gain 3.6. Before climate change After climate change Location Crop Profits Crop Profits Change in profits 0 Corn 0 N/A -- 0 1 Corn 4 N/A -- -4 2 Corn 6 Corn 0 -6 3 Corn 6 Corn 4.4 -1.6 4 Corn/wheat 4 Corn 6.6 2.6 5 Wheat 6 Corn 6.6 0.6 6 Wheat 6 Corn/wheat 4.4 -1.6 7 Wheat 4 Wheat 6.6 2.6 8 Wheat 0 Wheat 6.6 6.6 9 N/A -- Wheat 4.4 4.4 10 N/A -- Wheat 0 0 11 N/A -- N/A -- 0 12 N/A -- N/A -- 0 Sum 36 39.6 3.6
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c. Now 2 units land at L = 3, 4, 5, 6, and 1 unit of land at L = 7, 8, 9, 10, and 11 (we could safely assume 0 land at L = 0, 1, 2, and 12). Redo the table as below. We may see that the impact of climate change on the production pattern remains the same as before, i.e. locations 9 and 10 join the production, and locations 4, 5 and 6 switch from wheat to corn. Gainers and losers are also the same, however, locations 3 and 6’s losses doubled and locations 4 and 5’s gains also doubled.
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