A consumer has preferences over bundles of leisure (L) and consumption (z) respresented by the utility function u(L, r) = La and has 24 hours in the day to divide between work and lesiure. This consumer has some positive amount of nonwork income per day (m > 0) and is able to select how many hours they wish to work at some positive wage per hour (w> 0). Find the consumer's reservation wage as a function of m: this is the lowest wage at which the consumer will work positive hours. Equivalently, it is the highest wage at which the consumer will work zero hours. (Hint: this is all about the MRS when working zero hours.)

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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A consumer has preferences over bundles of leisure (L) and consumption (z) respresented by
the utility function u(L, r) = La and has 24 hours in the day to divide between work and
lesiure. This consumer has sorme positive amount of nonwork income per day (m > 0) and
is able to select how many hours they wish to work at some positive wage per hour (w > 0).
Find the consumer's reservation wage as a function of m: this is the lowest wage at which the
consumer will work positive hours. Equivalently, it is the highest wage at which the consumer
will work zero hours. (Hint: this is all about the MRS when working zero hours.)
Transcribed Image Text:A consumer has preferences over bundles of leisure (L) and consumption (z) respresented by the utility function u(L, r) = La and has 24 hours in the day to divide between work and lesiure. This consumer has sorme positive amount of nonwork income per day (m > 0) and is able to select how many hours they wish to work at some positive wage per hour (w > 0). Find the consumer's reservation wage as a function of m: this is the lowest wage at which the consumer will work positive hours. Equivalently, it is the highest wage at which the consumer will work zero hours. (Hint: this is all about the MRS when working zero hours.)
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