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# ch3_example1 - The marginal rate of substitution is equal...

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Natasha derives utility from attending rock concerts (r) and from colas (c) as follows: U(c,r) = c .9 r .1 The marginal utility of cola (MUc) and the marginal utility of rock concerts (MUr) are given as follows: MUc = .9c -.1 r .1 MUr = .1c .9 r -.9 a. If the price of cola (Pc) is \$1 and the price of concert tickets (Pr) is \$30 and Natasha's income is \$300, how many colas and tickets should Natasha buy to maximize utility? b. Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all. Under this constraint and given the prices and income in (a), how many colas and tickets should Natasha buy to maximize utility? c. Is Natasha better off under the conditions in (a) or (b)? Explain your answer. Solution: a. To maximize utility, Natasha (1) must be on her budget line, and (2) the marginal rate of substitution must equal the ratio of the prices of the goods.

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Unformatted text preview: The marginal rate of substitution is equal to the ratio of the marginal utilities of the goods. Thus: c + 30r = 300 MUc/MUr = (.9c-.1 r .1 )/(.1c .9 r-.9 ) = Pc/Pr = 1/30 Solving these equations simultaneously for c and r yields c = 270 and r = 1. b. Without the 4 ticket constraint, Natasha would prefer to buy just 1 ticket. If required to buy 4 tickets, Natasha would maximize utility by either buying 4 tickets and consuming 180 colas, or by buying zero tickets and consuming 300 colas. The utility function may be used to determine which is preferred. In this case, Natasha will buy 4 tickets and 180 colas. c. Natasha prefers (a). Constraining choice never leaves one better off. At best it has no effect. Otherwise, the addition of a constraint leaves one worse off....
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ch3_example1 - The marginal rate of substitution is equal...

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