Question

Consider the two-period model from Chapter 9, and assume there is one representative consumer with utility function uc,d) = Iníc) + In(d), so the time discount factor is 3 = 1. There is also a government that levies lump-sum taxes in the current and future periods. The government has expenditures of G = 580 in the current period and G' = 630 in the future period. (a) Suppose the consumer has current and future income (w.y') = (3500, 6510), and pays current and future taxes of it, t') = (600, 609). The real interest rate is r = 0.05. Solve the consumer's utility maximization problem for optimal consumption today and tomorrow, c, d, and calculate her savings, (b) Suppose that the government cuts taxes in the current period, but to balance the government's lifetime budget constraint taxes are raised in the future. The new tax schedule is (t2.) = (400,819). Verify that the government's present value budget constraint still holds. (c) Given the tax change above, solve the consumer's utility maximization problem for the new optimal consumption bundle (c. ) and savings . How doc. and compare to c, d, and se from part (a)? Are they the same or different? Explain why. (d) Using the current or future period government budget constraint, calculate the government borrowing or lending (i.e., the amount of government bonds, B) under each of the two possible tax policies above. (e) Bonus: From the perspective of the representative consumer, is one tax policy preferable to the other? Explain your answer.

Answer 1

(a) budgu onatnamt - -t.) 1+ n (3500-600)+GS10-609 C2 105 1.OS 2900+ 5620 - 8520 at aplinmal, MRS MU MUL P coneumpmnat purd P2 Pof omermpluon w2nd prnd Yer 1+91 14 -סי5c, m budgut onet 8520 105 29 862 0 Sy-t,-e)- 2900-42L0 CI-2O 4473 360 orbalancd budgut, anpendulure Toms 1180 400 + 810g Tanu, fuamt waue) np dulue(ruant nouu)560+ 630 105 1180 Tanu-unp noulive balancd budgul inprisent Hme walue

teo Lor thne nw tane t'-(400,819) conetraint budgue 1+ 3500-400) (CS10-819) 05 310 0+ 542 0 1.05 8108 8520 BC 2 852o 4260 S(3500-40o) -4260 11607 S amun ane moe m tn toa r diaa amngs au ues Ruason Lans drdut auet , Sbicauee alun lon, puam wa f bo the pod mcomy ummaun SO the allocalion tnat buven ahan Lame moe bucoat m I pumod, ans but aung ane ar nuducud omd dnapoaablu meomme is mas puied I

(d) 580 vaa Tan unume im I punod 6o0 2070 Ranemu npenditure nd ww.bamde 20 So geuernment B-20 Tan -180 0 Rnerwe-enpmduun 180 o, gant l barnos

i have solved first 4 parts of the question, marked from a) to d). please see the solution linewise.