Consider Susan who lives in a small town. A charity is planning to establish a public library in her town. Her total marginal benefit from the public library is MB=q(90-.6G½-.3g½), where G is the total number of books in the library, and g is her individual contribution, and q is the quality of the public library.How much would she contribute if others contribute 9,588 books, his perception of quality is q=⅓, and her marginal cost of giving is 10?Now assume that her contribution is tax-exempt and her marginal tax rate is 3%. How much would she contribute if others contribute 9,776 books, his perception of quality is q=⅓, and her marginal cost of giving is 10?Now assume that she realizes that 3% of her contribution goes to fundraising and other overhead costs. Her contribution is still tax-exempt, and her marginal tax rate is 3%. How much would she contribute if others contribute 9,693.25 books, her perception of quality is q=⅓, and her marginal cost is 10?

Marginal benefit (MB) refers to the additional benefit or utility that an individual receives from…

Answered: Consider Susan who lives in a small…

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

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Consider Susan who lives in a small town. A charity is planning to establish a public library in her town. Her total marginal benefit from the public library is MB=q(90-.6G½-.3g½), where G is the total number of books in the library, and g is her individual contribution, and q is the quality of the public library.

How much would she contribute if others contribute 9,588 books, his perception of quality is q=⅓, and her marginal cost of giving is 10?
Now assume that her contribution is tax-exempt and her marginal tax rate is 3%. How much would she contribute if others contribute 9,776 books, his perception of quality is q=⅓, and her marginal cost of giving is 10?
Now assume that she realizes that 3% of her contribution goes to fundraising and other overhead costs. Her contribution is still tax-exempt, and her marginal tax rate is 3%. How much would she contribute if others contribute 9,693.25 books, her perception of quality is q=⅓, and her marginal cost is 10?

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How did you arrive at -0.15 here?

MB = (1/3)(90 - 0.6(9,588 + g)^½- 0.3g^½)
To find Susan's optimal contribution, we need to calculate her marginal benefit, which is the derivative of MB with respect to g:
MB' = (1/3)(-0.15(9,588 + g)^(-1/2) - 0.15g^(-1/2))

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