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
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↑
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)
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
5
Q
How does we affect labour supply?
A
- Current leisure decreases when lifetime wealth increases
- C,C’,L,L’ are all normal goods
6
Q
What is MPC?
A
Slope of consumption demand vs current income: Marginal propensity to consume
7
Q
How does r affect consumption demand?
A
- ↑r → ↑s = ↓c
8
Q
What affect does we have on consumption demand?
A
- ↑we → ↑c
- As c is normal
9
Q
What is future capital for the firm in the full model?
A
K’ = (1-d)K + I
10
Q
What are the firms’ two profit equations in the full model?
A
- π = Y - wND - I
- 2. π’ = Y - w’N’D + (1-d)K’
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
12
Q
What is the firms labour decision when I > 0
A
πgross = π + I = Y - wND
13
Q
What is true of investments and dividends in the full model?
A
Increases in investment must be met by reduced dividend payments
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
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
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’
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
18
Q
What are the determinants of investment?
A
- r
- d
- ↑d → ↑I
- Must offset with more I
- Anything that effects MPK’
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
20
Q
How does K affect investment in the full model?
A
- K
- ↓K → ↑I
- b/c ↓K → ↑MPK’
21
Q
How does N affect investment in the full model?
A
- N
- ↑N → ↑I
- b/c ↑N → ↑MPK’
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
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
- G = T + B
- G’ + (1+r)B = T’
- PV BC
- G + (G’/(1+r)) = T + (T’/(1+r))
25
How is the credit market constructed in the full model?
- 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
How is the labour market constructed in the full model?
- 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
What are the exogenous shifters in the full model labour market?
* Supply
- Changes in G or G'
- Changes in r
* Demand
- Changes in TFP
28
How does an increase in G or G' affect the full model labour market?
- 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
How is the demand side of the goods market constructer in the full model?
- 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
What variables exogenously shift aggregate demand out in the full market?
- 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
How is the supply side of the goods market constructed in the full model?
- 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
What variables exogenously shift aggregate supply in the full market?
- 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
What are the inputs and output in the full model?
- Inputs: z, z’, K, G, G’
| - Outputs: N, Y, w, r, s, B, welfare
34
What is the methodology for using the full model?
- 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
What is the effect of a z increase on the full model?
- 1. z↑ → ND↑ = YS↑, πgross↑
- 2. π↑ → NS↓
- 3. r↓ → S(r)↓ → NS↓
- r↓ to clear the goods market
- An additional shift
- 4. w↑ to clear the labour market
- Result: Y↑, N↑, r↓, w↑, welfare↑
36
What is the overall effect of a z' increase on the full model?
- z’↑ → MPK’↑ → π’↑ = MB(I)↑ → I↑
- 1. z’ ↑ → I↑ = YD↑
- 2. π ↑ → NS↓
- Assume this is smaller than 3.
- 3. r↑ → S(r)↑→ NS↑
- r↑ to clear the goods market
- Assume r↑ → I↓ is smaller than 1.
- 4. w↓ to clear the labour market
- Result: Y↑, N↑, r↑, w↓
37
What extra variables are affected by a z' increase in the full model?
- Consumption
- C↓ because of r↑
- C↑ because of YD↑
- Ambiguous
- Investment
- I↑ because of z’↑
- I↓ because of r↑
- Overall increase
38
What is the effect of a permanent G increase in the full model?
- 1. G ↑ + C↓ → 0
- PIH: ΔG = ΔC since households not have to absorb ↑T
- 2. G ↑ = T↑, T’↑ → NS↑ = YS↑
- 3. r↓
- Since only YS shifting
- 4. NS(r1)↓ → NS(r2) back on itself
- Because . r↓ → ↓NS
- Result: Y↑, w↓, r↓
39
How is the multiplier related to an increase in G in the full model?
- 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
What is the effect of a K decrease in the full model?
- 1. ↓K → MPN↓ → ND↓ = YS↓
- 2. ↓K → I↑ = YD↑
- Assume that YS↓ > YD↑ so that Y↓
- 3. r↑ = c↓ + L↓
- 4. NS(r1)↑ → NS(r2)
- Result: Y↓, N↓, w↓, r↑
41
What is the effect of an increase in credit market uncertainty in the full model?
- Increases default premium
- 1. C↓ = YD↓
- 2. NS(r1)↓ → NS(r2)
- Result: N↓, w↑, Y↓, r↓
42
What is a sectoral shock?
- 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
What are mismatch friction wedges?
- 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
What is the effect of a sectoral shock in the full model?
- 1. Sectoral shock through wedge as and ad shifts labour supply and demand to the left, vertical distance being the wedges
- 2. Because N has fallen, YS shifts to the left
- Y↓(I+C), r↑, w stays the same, average product of labour increases
45
What is the average product of labour?
The slope of the line from the origin to the point of production on the firms production function
46
What would an increase in x, the default premium, do to a firm?
Shift the investment schedule in
47
What is the effect of a temporary increase in G in the full model?
- 1. G ↑ → YD↑
- ↓C (tax) + ↑G, MPC
- 2. G ↑ = T↑, T’↑ → NS↑ = YS↑
- 3. r↑ → S(r)↑→ NS↑
- r↑ to clear the goods market
- Assume YS shifts less than YD
- 4. 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
What is the full effect of a wage change?
- 1. ↑w → ↑c, ↓l, ↑NS (SE>IE)
| - 2. ↑w → ↑S → (-IE) ↓c,↓l = ↑NS at same wage rate
49
How does a change in z affect investment?
- z’↑ → MPK’↑ → π’↑ → MB(I)↑ → MB(I) > MC(I) → I↑
| - Or: (MPK’↑ + 1-d) / (1+r) = MB(I)↑
50
Why does a decrease in K lead to an increase in I?
- 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
When does a change in N affect YS?
- 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
What is the effect of a t'K' implementation with no ΔG or ΔT (revenue thrown away)?
- 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)}
- 2. π’↓ → we↓ → C↓, L↓ = NS(r1)↑ → YS↑
- NS(r1)↑ → YS↑ b/c no change to r
- 3. clearing r↓ → s↓ → C↑, L↑ = NS(r2)↓
- Result: Y↓, N↓, r↓, w↑
53
What is the effect of a t'K' implementation where T is lowered by T' remains the same?
- 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)}
- 2. Two effects
- A
- T↓ → we↑ → C↑, L↑ = NS(r1)↓
- NS(r1)↓ → YS↓ b/c no change to r
- B
- 2. 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
- 3. clearing r↓ → s↓ → C↑, L↑ = NS(r2)↓
- Result: Y↓, N↓, r↓, w↑
54
What is the effect of a tK with a reduction in T?
- No effect on MB(I) because current period
* 1. tk↑ → π↓ = -we = NS↑
- 2. T↓ = +we = NS↓
- Result: no effect on Y, N
55
What is the effect of a tK where the revenue is spent?
- 1. tk↑ → π↓ → NS↑ = YS↑
- 2. G↑ = YD↑
- 3. r↑ → NS↑
- 4. w↓
- Result: Y↑, N↑, r↑, w↓
