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11Breview7 - econ 11b ucsc ams 11b Review Questions 7...

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econ 11 b ucsc ams 11 b Review Questions 7 Applications of definite integrals to economics 1. Compute the following integrals. Use the table of integrals in Appendix C. a. Z 4 dx 5 x x 2 + 9 = b. Z 4 0 2 x dx 9 + 4 x = c. Z 10 0 200 t 2 e - 0 . 06 t dt = d. Z 3 dv 4 v 2 + 25 = e. Z 5 x 3 ln x dx = f. Z 2 0 3 + 5 x 2 + 7 x dx = 2. Compute the producers’ and consumers’ surplus at equilibrium for the market with the supply and demand equations: supply: p = 0 . 1 q + 5; demand: p = 40 - q 10 - q 2 100 . 3. Compute the Gini coefficient (of inequality) for the nation whose income distribu- tion curve is given by y = 0 . 3 x 3 + 0 . 2 x 2 + 0 . 5 x . 4. Compute the present value of the continuous annuity that pays at the rate f ( t ) =
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