Dynamic Model #3 Flashcards
Week 9
What is investment? When the RBC model includes Investment, how does this work?
- Capital (Stock) Vs. Investment (Flow)
- Investment is mainly undertaken by firms, including expenditure on plants, housing, machinery …
- Capital Market represents the tradeoff between current and future consumption -> real IR underlies in both
KM and CM, meaning that there is a balance between financial investment [CM] and physical investmnent [KM]
How can you calculate optimal C and C’ mathematically (WAY 1)?
- OPTIMISE: MaxU(C,h-N) + βU(C’,h-N)
- CONSTRAINTS: C + Sp = wN + π - T and C’ = w’N’ + π’ - T’ + (1+r)s
- Substituting out Sp, we get the lifetime :
C + C’ / (1+r) = w(h-l) + π - T + [w’(h-l’) + π’ - T’] / (1+r), where l/l’ = h-N/h-N’
Why is Sp not relevant to the lifetime budget constraint?
- Sp can only occur between consumers and Governments
- Consumer’s lending and borrowing ‘Nets out’
How else can you solve mathematically (CONS)?
- Substitute C and C’ and take partial derivatives of N, N’ and Sp (the three control variables)
- This then gives you 3 marginal conditions
- INTRA-> w=MRS (l,C) and w’=MRS (l’,C’)
- INTER -> 1+r = MRS (C,C’)
- Number of equations = number of unknowns
What are the graphical implications of each different marginal conditions (CONS)
- 1- w=MRS (l,C): w increases, MRS (l,C) increases, l falls, N increases- moves SoL upwards
- 2- w’=MRS (l’,C’): w’ increases, MRS (l’,C’) increases, l’ falls, N’ increases- moves SoL upwards
- 3- 1+r=MRS (C,C’): r increases, MRS (C,C’) increases, C falls, Sp increases- moves SoCredit upwards
If W_ is fixed, what does this mean?
- This makes the MRS (l,C) fixed as well,
- If C falls, this means that l will fall proportionally more
How can you find output for the representative firm?
- OBJECTIVE: Maxπ + π’ / (1+r) = Y - wN + I + (Y’ - w’N’ + I’) / (1+r)
- CONSTRAINTS: Y = zF(K,N) and Y’ = z’F(K’,N’), I = K’ - (1-δ)K
- Substituting out Y, Y’ and K’, we get the firms objective:
zF(K,N) - wN + I + “[z’F(I+{1-d}K, N] + [(1-d)(I+(1-d)k-w’N’)]” / 1+r
How else can you solve mathematically (PROD)?
- Take partial derivatives of N, N’ and I (the three endogenous variables)
- This then gives you 3 marginal conditions
- INTRA-> w=MPn and w’=MPn’
- INTER -> r+d = MPk’
What are the graphical implications of each different marginal conditions (PROD)
- 1- w=MPn : w increases, MPn increases, N falls due to DMP - moves DoL downwards
- 2- w’=MPn’ : w’ increases, MPn’ increases, N’ falls - moves DoL downwards
- 3- r + d=MPk’: r increases, MPk’ increases, k’ falls, I falls- moves DoCapital downwards
What would you expect to see on the 3rd producer marginal condition in times of financial crisis?
- “x” as a default risk premium
- r + “x” + d = MPk’
What are the different conditions required for each specific market to clear?
- LM=> Ns = Nd = N and N’s = N’d = N’
- CM=> Sp = B [THIS ONE IS REDUNDANT]
- KM => K’s = K’d = K’
- YM => zF(K,N) = Ys = Yd = C + I + G
How can intertemporal and intratemporal conditions combine into AD-AS framework? What causes shifts of curves?
- Combining intratemporal conditions between firms and consumers illustrates the relationship between r & Y
- AS = INTRA, Ys(r) = N *(r)
- AD = INTER, Yd(r) = C *(r) + I *(r) + G *(r)
- Using AD = AS, we can find equilibrium rates for r, Y, C and N
- If exogenous variables change, this shifts the curves
Explain the SRBC with respect to the two key schools of thought, considering the 2nd round effects
- CLASSICAL: Govt. should do nothing, z is not related
- Increasing z results in a boom, however, the income effect offsets the boom partially (2nd round feedback)
- KEYNESIAN: Govt. should do something
- Increase in G stimulates economy less than 1:1; δY / δG (2nd round effect from output market to input market)
Using symbols, Explain the key difference between Classical and Keynesian ideology?
- Classical: z increase, Nd increase, w&N increase, Ys increase, r decreasing and Ns falls
- Keynesian: Ns increase, w&N decrease, G increase, Yd increase, Ys increase, Ns increase, Ys increase…
