A microeconomist wants to determine how an individual's optimal choice of daily free time, represented by the function t*(w, I), responds to a small change in their hourly wage rate (w), assuming their unearned income (I) remains unchanged. Arrange the following steps into the correct logical sequence for conducting this analysis.
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An individual's optimal amount of daily free time, t*, is determined by their hourly wage rate (w) and their non-labor income (I). The relationship is given by the function: t*(w, I) = 12 + (0.5 * I) / w. Which of the following expressions correctly represents the rate at which the optimal amount of free time changes as the wage rate changes?
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Labor Supply Response to Policy Change
An individual's optimal choice for daily free time (t*) is described by the function t*(w, I) = 18 - (2w / I), where 'w' is the hourly wage rate and 'I' is daily unearned income. Assume both w and I are positive values. A student claims that for any positive wage and unearned income, a small increase in the wage rate will always lead to a decrease in the optimal amount of free time. Is this claim true or false?
An individual's optimal daily free time (t*) is a function of their hourly wage (w) and daily unearned income (I). Match each optimal free time function with the correct mathematical expression that represents how t* changes as the wage rate (w) changes, holding unearned income constant.
An individual's optimal daily free time, t*, is determined by their hourly wage, w, and daily unearned income, I, according to the function: t*(w, I) = 20 - 0.5*w + I/w. The mathematical expression that represents the rate of change of optimal free time with respect to the wage rate is ____.
A microeconomist wants to determine how an individual's optimal choice of daily free time, represented by the function t*(w, I), responds to a small change in their hourly wage rate (w), assuming their unearned income (I) remains unchanged. Arrange the following steps into the correct logical sequence for conducting this analysis.
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An economist observes that for a particular group of individuals, the rate at which their optimal daily free time (
t*) changes in response to a change in their hourly wage (w) is consistently represented by the expression-100/w². Given thatt*is a function of both wage (w) and unearned income (I), which of the following functions fort*is consistent with this observation?Comparing Economic Models of Labor-Leisure Choice