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Week 10: How to finance a war, and how to prevent temptations? (Optimal…

- - - - 1)Replace out the saving to get the intertemporal BC
        
        c1 + c2/(1+r) + c3/(1+r)^2 = y1 + y2/(1+r) + y3/(1+r)^2
      - 2)Replace c3 to solve unconstrained maximisation
        
        max u(c1) + bu(c2) + b^2u((1+r)^2(W-c1) - (1+r)c2)
    - - 2) r = 0
      - 3)u(c) = log(c)
        
        diminishing MRS
      - 1) beta = 1
        
        you like period 1 consumption as much as period 2 and period 3 consumptions
    - - max u(c1) + βu(c2) + β^2*u(c3) s.t. c1 + s1 = y1; c2 + s2 = y2 + s1(1+r); c3 = y3 + s2(1+r)
        
        |β|<1
        
        beta - how much you prefer consumption now to future consumption
      - W = y1 + y2/(1+r) + y3/(1+r)^2
    - - Properties
        
        Only total wealth matters
        
        Time profile of income {y1, y2, y3} doesn't matter
        
        can borrow\lend to finance his/her consumption
        
        only permanent income W matter for consumption, not current income y
        
        Consumption smoothing
        
        people want to smooth consumption over time
        
        Use borrowing/lending to achieve it
      - c1 = c2 = c3 = W/3
      - use FOCs
  - - - W = y1 - t1 + (y2 - t2) + (y3 - t3) = (y1 + y2+ y3) - (g1 + g2 + g3)
        
        if you raise t1, you need to lower t2
    - - The time profile of {t1, t2, t3} doesn't matter for consumption
        
        All that matters for consumption is the total government purchases
        
        e.g. if t2 is too high, a consumer will just save more in period 1 or borrow from period 3
        
        Consumption smoothing cancels out gov. budget manipulations with public saving/borrowing
    - - g1 + g2 + g3 = t1 + t2 + t3
      - r = 0
    - - introduce distortionary taxes
- - - - log(c1) + log(c2) + log(c3)
        
        Combine budget constraint of consumers and
        government to get to the overall resource
        constraint of the economy
        
        c1 + c2 + c3 = W - g
  - - - max log(c1) + log(c2) + log(c3)
        s.t.c1 + c2 + c3 = W - g
        
        Solution: consume the same in every period (consumption smoothing) + tax the same in every period (tax smoothing)
  - - - Pay for war with debt
- - - - U(c1 ,c2 ,c3 ) = δ log(c1) + log(c2 ) + log(c3 )
        U(c2 ,c3 ) = δ log(c2 ) + log(c3 )
        
        With delta>1 capturing the salience of the present.
        
        solution: c1> c2> c3
        
        Dynamic inconsistency
    - - You choose / plan to do it tomorrow when it costs less.
        
        You procrastinate, because present is always so
        costly
    - - Now, today you are smart. You know you are going to be
        tempted tomorrow
        
        Option 1: Force your tomorrow self to do it
        
        Increase the cost of not doing it later
        
        Option 2: do it today
        
        Realize that the cost of doing it now is lower than in future
        
        Option 3: tie yourself to the mast
        
        Split savings of ½ into liquid savings available at date
        2, and illiquid savings that can only touch at date 3
        
        Making splurging expensive leads to same
        consumption as tying yourself to the mast
    - - u(c1, c2, c3) = lnc1 + ln c2 + lnc3
  - - - Extra discounting comes from probability will not be
        in power
        
        Personal self-control compounded by the election
        incentives and desire to pursue your agenda before
        leaving office
        
        Solutions: • Commitment strategies: limits of government,
        constitutional rules.
        
        Option 1: Paternalism
        
        Join European Union, blame Brussels.
        
        Sign pacts, troika deals, bypass democracy
        
        Option 2:Tied to mast:
        
        Balanced budget rules
        
        Option 3:Raise borrowing costs:
        
        Constraints on bond issuance, debt limits
        
        Spending cuts or tax increases are politically painful,
        always delay it until tomorrow, when may or may
        not be in power
        
        More radical government, least likely to pay for bill,
        will want to borrow more to favor its interests.