A representative household receives utility from consumption c and supplying labor I: u{c,l} =1og c -l- galog i) As usual, I is the share of time that the household spends working. The household owns an exogenouslyr 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)Wl-l-Rk Solve the household's utility maximization problem and derive the household's labor supply.I equation that expresses E as a function ofthe real wage W/P, the real rental rate RIP, capital it\Suppose that the government raises the labor income tax rate 1'. Everything else equal, will the household supply more or less labor? Explain in words the intuition behind this result