Suppose a representative worker in the economy has preferences over consumption and leisure that can be represented by the following utility function: ???? = ln(????) + ln(????)
,where ???? is consumption and ???? is leisure. Time endowment for this individual is 16 hrs (i.e. ???? + ???? = 16, ???? is the working time). The hourly wage is ????, and we assume that the price of each unit of consumption is $1. Labor income is the only source of income.

(a) Write down the worker’s budget constraint in terms of ???? and ????.

(b) Find the optimal consumption and work as a function of ????.

(c) Now suppose there are 100 workers identical to the one we analyzed. There are also 200 firms, each one with a production function ???? = 4???? − ????2. Suppose that the price of the firms’ output is $1 per unit. Find the labor supply and labor demand curves (for this economy), and use them to find the equilibrium wage and labor.

 

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a The workers budget constraint can be expressed as the total income being equal to the total expend... View the full answer