Question: A representative household receives utility from consumption c and supplying labor I: u(c,l} = log c+ golog E] As usualJ is the share of time

A representative household receives utility from consumption c and supplying labor I: u(c,l} = log c+ golog E] As usualJ is the share of time that the household spends working. The household owns an exogenously determined amount of capital it, earns the nominal rental rate R on each unit of its capital holdings, earns the nominal wage W on each unit of labor it supplies, and pays the price P per unit of consumption. However, now suppose that the household pays an exogenous tax rate '3' on labor income. The household's budget constraint is therefore: Pc 2 [1 T)WI-l- RR: Solve the household's utility maximization problem and derive the household's labor supply equation that expresses I as a function ofthe real wage W/P, the real rental rate R/P, capital It, the labor income tax rate 1", and the utility function parameter 4,0

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