TERM 1: CA & production economy Flashcards
What do firms do in periods 1 and 2?
Period 1 = invest in physical capital
Period 2 = use capital to produce goods (Q2)
Production function period 2
Q2 = A2 F(I1)
Properties of production function (3)
- F(0)=0
- F’ > 0 - increasing
- F’’ < 0 - concave = diminishing MPK
MPK =
A2 F’(I1)
How do firms finance purchases of K in period 1?
Borrow: D1F = I1
Borrow at IR r1
Firms repayments
(1+r1)D1f
Period 2 profits
Pi2 = A2F(I1) - (1+r1)D1f or I1 since D1F=I1
Optimal investment
A2F'(I1) = (1+r1) MPK = marginal cost of investment (constant)
Impact of change in IR and efficiency on investment schedule
change in r1 = move along investment schedule
change in A2 = shift
Period 1 profits
Pi1 = A1F(I0) - (1+r0)D0f
Can firms effect P1 profits?
NO because all parameters exogenous
How do households relate to firms?
Households OWN firms
Period 1 BC household
C1 + (B1h - B0h) = r0B0h + Pi1
Period 2 BC households
C2 + (B2h - B1h) = r1B1h + Pi2
Optimality/transversatility condition
B2h=0
Economy’s intertemporal resource constraint
C1 + C2/(1+r1) + I1 = (1+r0)B0* + A1F(I0) + A2F(I1)/(1+r1)
B0* =
B1h - D1f
small open economy means
r1=r*
optimal consumption
U1(C1, C2)/U2(C1, C2) = (1+r1)
MRS = MC of C1
slope of IC = slope of BC
TB1 =
TB1 = Q1 - C1 - I1
CA1 =
CA1 = r0B0* + TB1
TB2 =
TB2 = Q2 - C2 (I2 = 0)
End of p1 investment (2 ways)
B1* = B0* + CA1
or B1* = (1+r0)B0* + TB1
CA2 =
CA2 = r1B1* + TB2
National savings =
S1 = Q1 + r0B0* - C1
where Q1 = A1 F(I0)
3 effects of higher IR
- SE: rise r1, fall C1
- IE on household debt: rise r1, fall C1 for debtors (B0h<0); rise C1 for lenders (B0h>0)
- IE on profits: rise r1, fall Pi2 = fall C1
Which effect dominates? Therefore impact of IR on saving is…?
SE>IE
Therefore: higher r1 = lower C1 = higher S1
National savings rise
What is a collateral constraint?
Firms can borrow at most k units in period 1:
D1f<=k
Constrained equilibrium under collateral constraint
I1 = MIN{I1NC, k}
Where I1NC satisfies: A2F’(I1) = (1+r1)
