10 logging firms use a forest to collect timber. Each firm must choose how many trees to cut, 9;. The benefit of cutting a tree is 1000-2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. The social optimum solves: max(1000-2G)G-10G O O max (1000-2G)G-5G² O max 9, (1000-2G)g₁ - 10g; 9₁ O max (1000-2G)g, -5g?
10 logging firms use a forest to collect timber. Each firm must choose how many trees to cut, 9;. The benefit of cutting a tree is 1000-2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. The social optimum solves: max(1000-2G)G-10G O O max (1000-2G)G-5G² O max 9, (1000-2G)g₁ - 10g; 9₁ O max (1000-2G)g, -5g?
Chapter4: Systems Of Linear Equations
Section4.3: Solve Mixture Applications With Systems Of Equations
Problem 159E: The manufacturer of a water bottle spends $5 to build each bottle and sells them for $10. The...
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Transcribed Image Text:10 logging firms use a forest to collect timber. Each firm must choose how many trees to
cut, 9₁. The benefit of cutting a tree is 1000-2G per tree, where G is the total
quantity of trees cut in the forest. The marginal cost of cutting a tree is 100. Firms do not
face any fixed costs. The social optimum solves:
O max (1000-2G)G-10G
O max(1000-2G)G-5G²
O max, (1000-2G)g₁ - 10g;
O max, (1000-2G)g;- 5g7
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