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Macroeconomics Exam Review 225

Macroeconomics Exam Review 225 - Solutions for Foundations...

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Chapter 5: Optimization 5.1 As stated, this problem has no optimal solution. Revenue 𝑓 ( 𝑥 ) increases without bound as the rate of exploitation 𝑥 gets smaller and smaller. Given any positive ex- ploitation rate 𝑥 0 , a smaller rate will increase total revenue. Nonexistence arises from inadequacy in modeling the island leaders’ problem. For example, the model ignores any costs of extraction and sale. Realistically, we would expect per-unit costs to de- crease with volume (increasing returns to scale) at least over lower outputs. Extraction and transaction costs should make vanishingly small rates of output prohibitively ex- pensive and encourage faster utilization. Secondly, even if the government weights future generations equally with the current generation, it would be rational to value current revenue more highly than future revenue and discount future returns. Dis- counting is appropriate for two reasons Current revenues can be invested to provide a future return. There is an oppor- tunity cost (the interest foregone) to delaying extraction and sale.
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