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ECON2102S2 > Real Intertemporal Model With Investment > Flashcards

Real Intertemporal Model With Investment Flashcards

1
Q

What is the consumers budget constant in the real inter temporal model?

A

c = w(h-l) + π - T - s

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2
Q

What is the effect of an increase in savings on the consumers budget constant in the full inter temporal model?

A
  • ↓C

- ↓l → Ns↑

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3
Q

What effect does the interest rate have on labour supply?

A
  • An increase in r increases current labour supply
    • Inter temporal substitution of leisure
    • Increases labour so can save more and consume more in future (takes advantage of the fall in price)
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4
Q

What is the current price of leisure relative to the future price?

A
  • (w(1+r))/w’
  • Therefore an increase in r given w and w’ results in in increase in the price of current leisure relative to future leisure
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5
Q

How does we affect labour supply?

A
  • Current leisure decreases when lifetime wealth increases

- C,C’,L,L’ are all normal goods

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6
Q

What is MPC?

A

Slope of consumption demand vs current income: Marginal propensity to consume

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7
Q

How does r affect consumption demand?

A
  • ↑r → ↑s = ↓c
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8
Q

What affect does we have on consumption demand?

A
  • ↑we → ↑c

- As c is normal

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9
Q

What is future capital for the firm in the full model?

A

K’ = (1-d)K + I

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10
Q

What are the firms’ two profit equations in the full model?

A
    1. π = Y - wND - I

- 2. π’ = Y - w’N’D + (1-d)K’

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11
Q

What is V and what does this represent?

A
  • V = π + π’/(1+r)
  • Present value of profit
  • Firm tries to maximise this by choosing N, N’ and I
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12
Q

What is the firms labour decision when I > 0

A

πgross = π + I = Y - wND

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13
Q

What is true of investments and dividends in the full model?

A

Increases in investment must be met by reduced dividend payments

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14
Q

What is MC(I)?

A
  • Marginal Cost of investment = 1
    • MC(I) for the firm is what it gives up, in terms of the present value of profits V, by investing in one unit of capital in the current period.
    • This works out to be 1
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15
Q

What is MB(I)?

A
  • Marginal benefit of investment: (MPK’ + (1-d))/(1+r)

- What one extra I in current period adds to the present value of profits V

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16
Q

What is the firms optimal investment rule?

A
  • MPK’ - d = r
    • Net Marginal product of capital = the real interest rate
    • Determines a negative relationship between K’ and r: if r↑ then the firm will choose a smaller K’ so as to increase MPK’
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17
Q

What is the optimal investment schedule?

A
  • The firm’s net marginal product of capital as a function of
    investment given the initial quantity of capital K
    • relationship between r and I
  • Line called MPK’ - d
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18
Q

What are the determinants of investment?

A
  • r
  • d
    • ↑d → ↑I
    • Must offset with more I
  • Anything that effects MPK’
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19
Q

How does z’ affect investment in the full model?

A
  • z’
    • ↑z’ → ↑I
    • If z is expected to be higher in the future we would invest more
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20
Q

How does K affect investment in the full model?

A
  • K
    • ↓K → ↑I
    • b/c ↓K → ↑MPK’
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21
Q

How does N affect investment in the full model?

A
  • N
    • ↑N → ↑I
    • b/c ↑N → ↑MPK’
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22
Q

How do credit market frictions affect the firms investment decision in the full model?

A
  • Bad firms vs good firms - asymmetric information: rloan - rlending = x, default premium, interest rate spread
  • x would increase during crisis
  • For firms that borrow to invest, MPK’ - x - d = r
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23
Q

What is the firm’s second period decision in the full model?

A
  • K’ = (1-d)K + I
  • Y’ = z’F(K’,N’)
  • Only decision to be made is N’
  • π’ = Y - w’N’ + (1-d)K’
24
Q

What is the governments budget constraints in the full model?

A
    1. G = T + B
    1. G’ + (1+r)B = T’
  • PV BC
    • G + (G’/(1+r)) = T + (T’/(1+r))
25
Q

How is the credit market constructed in the full model?

A
  • Consumption/savings decision determines supply in the market, and we assume that on average households are savers. SE > IE when r changes means S(G) is upward sloping
  • Government borrowing is exogenous and perfectly elastic
26
Q

How is the labour market constructed in the full model?

A
  • Consumption/leisure decision determines supply in the market. SE > IE when w changes means Ns is upward sloping
  • Firms profit maximisation decision determines Nd, which increases as w falls
27
Q

What are the exogenous shifters in the full model labour market?

A
  • Supply
    • Changes in G or G’
    • Changes in r
  • Demand
    • Changes in TFP
28
Q

How does an increase in G or G’ affect the full model labour market?

A
  • Causes a decrease in we (through increased T or T’)
  • Causes a decrease in leisure and a labour supply shift to the right
  • Lower wages and higher Y at the same r
29
Q

How is the demand side of the goods market constructer in the full model?

A
  • Consumption
    • Consumers tend to decrease current consumption when interest rates rise as borrowing to purchase is more expensive and there is a higher incentive to save
  • Investment
    • Lower r: MB > MC
    • Higher r: MB
30
Q

What variables exogenously shift aggregate demand out in the full market?

A
  • Decrease in PV of T
    • Through increase in we: increase in c
  • Increase in Y’
    • If income is anticipated to increase, we increases
  • Increase in z’
    • Through investment
  • Decrease in K
    • Though investment
  • Increase in G
    • Though G
31
Q

How is the supply side of the goods market constructed in the full model?

A
  • For a given r, we have a given labour supply curve
  • An increased r will shift the labour supply curve out - inter temporal substitution of leisure
  • The will lead to the firm increasing output
32
Q

What variables exogenously shift aggregate supply in the full market?

A
  • Shifts due to change in the production function, the labour demand curve or the labour supply curve (though not arising because of a change in r, the output supply already takes this into account)
  • Lifetime Wealth
    • Increase in G or G’ = increase in lifetime T burden: decrease in we
    • Decreases in we shifts labour supply out, employment increases for a given r, and output shifts out as well
  • TFP or K
    • Increase in z or K causes production function to shift up, labour demand shifts out, output shifts out
33
Q

What are the inputs and output in the full model?

A
  • Inputs: z, z’, K, G, G’

- Outputs: N, Y, w, r, s, B, welfare

34
Q

What is the methodology for using the full model?

A
  • Determine current equilibrium
  • Identify exogenous variable changes and the curves that depend on that variable
  • Find the new market-clearing real interest rate
  • Shift curves that depend on real interest rate
  • Find new equilibrium and find endogenous variable changes
35
Q

What is the effect of a z increase on the full model?

A
    1. z↑ → ND↑ = YS↑, πgross↑
    1. π↑ → NS↓
    1. r↓ → S(r)↓ → NS↓
      - r↓ to clear the goods market
      - An additional shift
    1. w↑ to clear the labour market
  • Result: Y↑, N↑, r↓, w↑, welfare↑
36
Q

What is the overall effect of a z’ increase on the full model?

A
  • z’↑ → MPK’↑ → π’↑ = MB(I)↑ → I↑
    1. z’ ↑ → I↑ = YD↑
    1. π ↑ → NS↓
      - Assume this is smaller than 3.
    1. r↑ → S(r)↑→ NS↑
      - r↑ to clear the goods market
      - Assume r↑ → I↓ is smaller than 1.
    1. w↓ to clear the labour market
  • Result: Y↑, N↑, r↑, w↓
37
Q

What extra variables are affected by a z’ increase in the full model?

A
  • Consumption
    • C↓ because of r↑
    • C↑ because of YD↑
    • Ambiguous
  • Investment
    • I↑ because of z’↑
    • I↓ because of r↑
    • Overall increase
38
Q

What is the effect of a permanent G increase in the full model?

A
    1. G ↑ + C↓ → 0
      - PIH: ΔG = ΔC since households not have to absorb ↑T
    1. G ↑ = T↑, T’↑ → NS↑ = YS↑
    1. r↓
      - Since only YS shifting
    1. NS(r1)↓ → NS(r2) back on itself
      - Because . r↓ → ↓NS
  • Result: Y↑, w↓, r↓
39
Q

How is the multiplier related to an increase in G in the full model?

A
  • The total multiplier ratio of equilibrium increase in Y to the
    increase in G must be less than 1
    • Horizontal YD↑ vs increase to equilibrium
  • Extra G comes at a cost: crowds out C and I, and we all have to work harder
  • In Keynesian analysis, multiplier is greater than 1 because the analysis does not take account of how the extra output is to be producer and the effect of T and T’ on consumption
40
Q

What is the effect of a K decrease in the full model?

A
    1. ↓K → MPN↓ → ND↓ = YS↓
    1. ↓K → I↑ = YD↑
      - Assume that YS↓ > YD↑ so that Y↓
    1. r↑ = c↓ + L↓
    1. NS(r1)↑ → NS(r2)
  • Result: Y↓, N↓, w↓, r↑
41
Q

What is the effect of an increase in credit market uncertainty in the full model?

A
  • Increases default premium
    1. C↓ = YD↓
    1. NS(r1)↓ → NS(r2)
  • Result: N↓, w↑, Y↓, r↓
42
Q

What is a sectoral shock?

A
  • A disturbance to tech or preferences, which either changes relaitve TFP in different sectors or changes relative demands for goods and services produced in different sectors
  • Produce a reallocation of factors of production from declining sectors to growing sectors, and that can take time
43
Q

What are mismatch friction wedges?

A
  • as is the cost a worker bears for entering the labour market, proportional to the quantity of labour supplied, so that the effective wage a worker receives is w - as
  • ad is the cost a firm must bear for finding suitable labour, proportional to the quantity of labour hired so that the effective wage the firm pays is w + ad
  • The difference between what the firm pays for labour and what the worker receives is as + ad
44
Q

What is the effect of a sectoral shock in the full model?

A
    1. Sectoral shock through wedge as and ad shifts labour supply and demand to the left, vertical distance being the wedges
    1. Because N has fallen, YS shifts to the left
  • Y↓(I+C), r↑, w stays the same, average product of labour increases
45
Q

What is the average product of labour?

A

The slope of the line from the origin to the point of production on the firms production function

46
Q

What would an increase in x, the default premium, do to a firm?

A

Shift the investment schedule in

47
Q

What is the effect of a temporary increase in G in the full model?

A
    1. G ↑ → YD↑
      - ↓C (tax) + ↑G, MPC
    1. G ↑ = T↑, T’↑ → NS↑ = YS↑
    1. r↑ → S(r)↑→ NS↑
      - r↑ to clear the goods market
      • Assume YS shifts less than YD
    1. w↓ to clear the labour market
  • Result: Y↑, N↑, r↑, w↓, C↓
    • Crowding out of private C and investment since it is now more expensive, therefore overall effect is also to lower K’
48
Q

What is the full effect of a wage change?

A
    1. ↑w → ↑c, ↓l, ↑NS (SE>IE)

- 2. ↑w → ↑S → (-IE) ↓c,↓l = ↑NS at same wage rate

49
Q

How does a change in z affect investment?

A
  • z’↑ → MPK’↑ → π’↑ → MB(I)↑ → MB(I) > MC(I) → I↑

- Or: (MPK’↑ + 1-d) / (1+r) = MB(I)↑

50
Q

Why does a decrease in K lead to an increase in I?

A
  • b/c ↓K → K’↓ → ↑MPK’ → MB(I)↑ → I↑
  • K’ = (1-d)K + I
    • MPK’ = αz’ ((N’)^1-α/(K’)^1-α)
    • so ↓MPK’↓ = αz’ ((N’)^1-α/↓(K’)^1-α)↓
51
Q

When does a change in N affect YS?

A
  • When the change in NS isn’t due to r

- IF NS AND ND BOTH CHANGE THEN LOOK AT OVERALL N CHANGE TO DETERMINE EFFECT ON Y

52
Q

What is the effect of a t’K’ implementation with no ΔG or ΔT (revenue thrown away)?

A
    1. t’K’↑ → π’↓ → MB(I)↓ → I↓ = YD↓
      - b/c {MB(I)old = (MPK’ + (1-d))/(1+r)} > {MB(I)new = (MPK’ +
      (1-d-t’))/(1+r)}
    1. π’↓ → we↓ → C↓, L↓ = NS(r1)↑ → YS↑
      - NS(r1)↑ → YS↑ b/c no change to r
    1. clearing r↓ → s↓ → C↑, L↑ = NS(r2)↓
  • Result: Y↓, N↓, r↓, w↑
53
Q

What is the effect of a t’K’ implementation where T is lowered by T’ remains the same?

A
    1. t’K’↑ → π’↓ → MB(I)↓ → I↓ = YD↓
      - b/c {MB(I)old = (MPK’ + (1-d))/(1+r)} > {MB(I)new = (MPK’ +
      (1-d-t’))/(1+r)}
    1. Two effects
      - A
      • T↓ → we↑ → C↑, L↑ = NS(r1)↓
      • NS(r1)↓ → YS↓ b/c no change to r
        - B
        1. π’↓ → we↓ → C↓, L↓ = NS(r1)↑ → YS↑
      • NS(r1)↑ → YS↑ b/c no change to r
        - Assume A = B so that ΔT = -Δ((t’K’)/(1+r)) so 0Δ overall
    1. clearing r↓ → s↓ → C↑, L↑ = NS(r2)↓
  • Result: Y↓, N↓, r↓, w↑
54
Q

What is the effect of a tK with a reduction in T?

A
  • No effect on MB(I) because current period
    1. tk↑ → π↓ = -we = NS↑
    1. T↓ = +we = NS↓
  • Result: no effect on Y, N
55
Q

What is the effect of a tK where the revenue is spent?

A
    1. tk↑ → π↓ → NS↑ = YS↑
    1. G↑ = YD↑
    1. r↑ → NS↑
    1. w↓
  • Result: Y↑, N↑, r↑, w↓

ECON2102S2 (6 decks)

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