Consider an economy with two goods, consumption c and leisure l, and a representative consumer. The...

 

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Consider an economy with two goods, consumption c and leisure l, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal tol = 24 – h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hl+ hours of work can be represented by the utility function U(c, h) = c - 1+ (a) What is this consumer's budget constraint? (b) Solve for the consumer's utility maximizing hours of work h*(w, 1- T, Y) and con- sumption c*(w,1– 1, Y). (c) Repeat part (b) for a consumer with the utility function U (c, h) = alog(c)- Blog(h). Consider an economy with two goods, consumption c and leisure l, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal tol = 24 – h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of T percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hl+ hours of work can be represented by the utility function U(c, h) = c - 1+ (a) What is this consumer's budget constraint? (b) Solve for the consumer's utility maximizing hours of work h*(w, 1- T, Y) and con- sumption c*(w,1– 1, Y). (c) Repeat part (b) for a consumer with the utility function U (c, h) = alog(c)- Blog(h).

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a Budget constraint will be c w1th 24Y where I am taking ... View the full answer