Question

1. This problem asks you to consider the effects of a distortionary tax on consumption. Let utility be given by U = Inc+ ß In c' with budget constraints c(1+t) = yes d' (1+t) = y +s (1+r). (a) Solve the budget constraints for c and d and substitute the resulting expressions into utility, writing utility as a function of s. Maximize utility with respect to s. Write an expression for the Euler equation. (b) Does the distortionary tax affect the choice of current relative to future consump- tion? Explain.

Answer 1

fox on Consumption then x Given collect from the data of let us assume that the equations are * To consider the effects of distantary given by Now Us Inc + Band - -> The Budget constraints CC14t)=y-and c'C14t) =y'tsCity) Clitory yo @ the budget constraints of cand di are the substitute the resu expresion into utility these function has us. Now cli+t)=y-s > 3 and écrit) - Y'+sc1+3) > 0 from and from @ → C = (yes) CI+) City = =cyts)(1+r)/ +4) Now we have to substitute me values of cand ca ve In CCY-S)C1+t)]+ Bin[{y'_s)(1+y)(1++)] let us Maximum u with respect to so ole so low -"0-5)+ (B/y45CHY)/1+1)] -0 aleb Os the u function have Maximum ay s= /Q+B) v-[1/64B) Now v= In [fy-s)- In C+b) + Binc y4s(1+y)-ß In Cht) © The distro ninong terk affect the choice of current relative to future consumption.

of conuntion will influence & They 1. The are present decision future decision * it will be realize that the controotion seems to be "any take off from the perfect of flawless challenge in the way middles with The Monetary operators boosting social welfare in the expand their own. * It will aggrenive harmony, corresponding pay annual assessment disheartnes work, all the more by the large Proportions social cost twist in to the Market cost it will be such deviation decent and its neglible may offer ascent to in this manner, it will right influence future consumption L THE END - >