1. Household Labor Supply and Consumption Tax Consider a houschold with capital k0 solving the following labor supply problem with given prices w,r : mixetU(c,1l)(1+)c(1)ulc0,l[0,1], where e represents a consumption tax and a labor income tax. Assume that the government consumes the tax revenue directly; that is, TeC+=g A firm operates a technology and hires labor to maximize profits, where profits are given as (k,l)=Altawl 1. Define an equilibrium for this economy. 2. Assume: U(c,1l)=log(c)+21log(1l),A=1,a=1/3,Tc=0.10, and =0.25. Characterize the equilibrium (solve it) as much as possible. 3. Now take the same parameters from above but assume CRRA utility: U(c,l)=1c11+t1+0 Suppose that instead of consuming the tax revente directly, the government transfers income to the houschold; that is, cc+wl=T and the household budget constraint is now written as (1+c)c=(11)wl+T. Write down the set of equations that characterize the equilibrium. 4. Bonus. Briefly describe the steps of how you would compute the equilibrium T that is consistent with the household's budget constraint and balances the government budget constraint. 1. Household Labor Supply and Consumption Tax Consider a houschold with capital k0 solving the following labor supply problem with given prices w,r : mixetU(c,1l)(1+)c(1)ulc0,l[0,1], where e represents a consumption tax and a labor income tax. Assume that the government consumes the tax revenue directly; that is, TeC+=g A firm operates a technology and hires labor to maximize profits, where profits are given as (k,l)=Altawl 1. Define an equilibrium for this economy. 2. Assume: U(c,1l)=log(c)+21log(1l),A=1,a=1/3,Tc=0.10, and =0.25. Characterize the equilibrium (solve it) as much as possible. 3. Now take the same parameters from above but assume CRRA utility: U(c,l)=1c11+t1+0 Suppose that instead of consuming the tax revente directly, the government transfers income to the houschold; that is, cc+wl=T and the household budget constraint is now written as (1+c)c=(11)wl+T. Write down the set of equations that characterize the equilibrium. 4. Bonus. Briefly describe the steps of how you would compute the equilibrium T that is consistent with the household's budget constraint and balances the government budget constraint