Week 4 Production Flashcards
How does adding production to the simple free open economy model change the analysis?
It now further looks at how investment decisions can impact CA.
How does the production economy model work? (For two periods).
Firms invest in capital in period 1 and this is used for production in period 2.
- What is Q2 in the production economy?
2.How does it contrast to previous? - Break down each part of Q2
Previously endowment just fell from the sky.
Now Q2 = A2 . F(I1)
- A2 > 0 and is an efficiency parameter.
So the same amount of machines can produce more.
F(.) is an increasing and concave function.
What are the important features of F(.)?
Increasing and concave
i : F(0) = (0) no investment will lead to no production
ii : F(.)’ > 0 Increasing function.
iii : F(.)’’ < 0 Rate of change is decreasing.
What is the MPK in the production model?
Extra unit of capital that is brought by an extra unit of machine. MPK = A2 F’(I1).
Draw and describe what the production function looks like and what the MPK looks like?
Production function:
x axis = investment
y axis = Q2
it is an upward sloping line going from bottom left to top right.
MPK function =
X axis = investment
Y axis = MPK downward sloping. Top left to bottom right.
What is the MPK at 0?
It is infinity as you move from no production to production.
What is the impact of an increase in the efficiency parameter on production function and MPK.
It tilts the production function upwards.
Has no effect when = 0 but gap gets bigger as I1 increases.
MPK is increasing in efficiency so it moves out.
In simple production model how to firms buy machines?
They invest and take on debt
I1 = df1
They borrow at interest rate r
They repay the loan in period 2
so df1(1+r).
What are the profits for the firm in period 2.
What is the optimal investment?
Explain this
Pi2 = A2 F(I1) - (1+r1)Df1
Diff W.R.T investment A2 F’(I1) = (1+r1).
Optimal investment makes marginal product of capital = to the marginal cost of capital.
Graphically what does the MPK and MC graphs look like.
Draw this.
MPK is the classic downward sloping line
MC is horizontal and constant
Where they meet is optimal investment.
Graphically how does an increase in interest rate shift the optimal investment decision.
Increase in interest rate shifts the MC curve up which then moves I1 to the left (which is less investment).
Cost of capital is increasing while benefits of capital are the same.
Graphically how does an increase in efficiency impact optimal investment decision.
higher efficiency causes MPK to shift up.
Whilst cost does not change
This makes I1 increase.
What is the investment schedule graphically?
X axis = investment
Y axis = interest rate
Downward sloping curve that is shifted up by increased efficiency.Wh
What is the profit in period 1 and what is the importance of this within the model?
Pi1 = A1 . F(I0) - (1+r0)Df0
However, there was no one alive in period 0 to make this so all these variables are pre-determined.
Firm cannot impact profits in period 1.
What is an important caveat between households and firms in the production economy?
Households own firms.
Profits made by firms goes back to households.
What is the budget constraint for the production economy in period 1 and period 2? FOR HOUSEHOLDS.
How do you get the IBC?
C1 + Bh1 - Bh0 = pi1 + r0Bh0
C2 + Bh2 - Bh1 = pi2 +r1Bh1
Bh2 = 0 as previously discussed
Then eliminate Bh1
What is the Net inital investment position in the production economy?
Explain the reasoning about this?
B*0 = Bh0 - Df0
This is because the production economy is made up of households and firms.
Therefore, the debt is household debt + Firm debt.
How do you go from households intertemproral budget constraint to the Economy Intertemoral budget constraint.
Explain each part.
You start with the household IBC:
C1 + C2 / 1+r1 = pi1 + pi2 / 1+r1 + (1+r0)Bh0
You then sub in equation for pi1 and pi2
You then sub in equation for bh0
This yields
C1 + C2/1+r1 + I1 = A1F(I0) + A2F(I1)/ 1+r1 + (1+r0)B*0
LHS is presented discounted expenditure
RHS is present discounted wealth.
What is the equilibrium in a production economy?
r1 = r*
A2.F’(I1) = (1+r1)
MRS = 1+r
C1 + C2/1+r1 + I1 = A1F(I0) + A2F(I1)/ 1+r1 + (1+r0)B*0
Given the other exogenous variables as well you can solve for the unknowns.
- What is output in period 1 in the Production economy model?
- What is TB1 in production economy?
- What is CA1 in production economy?
- What is output in period 2 in production economy.
- What is TB2 in production economy?
1.Q1 = A1 . F(I0)
2.TB1 = Q1 - C1 - I1
3.CA1 = TB1 + r0B*0
- Q2 = A2 . F (I1)
- TB2 = Q2 - C1
What is the NIIP at the end of period 1 in production economy?
What is the current account in period 2?
What are national savings?
- B1 = CA1 + B0
- CA2 = TB2 + r1B*1
- S1 = Q1 + r0B*0 - C1
Focusing on the TB1 formula state it and explain why it works?
TB1 = Q1 - C1 - I1
This is because if C1 + I1 > Q1 it means that the country is importing from abroad.
How does interest rate now impact consumption in production economy model and what equation explains this?
S1 = Q1 + r0B*0 - C1
Substitution effect - if r0 increases people prefer to save so consumption decreases
Income/ wealth effect
For creditors , income is higher as they are getting paid more on the debt owed to them. Consumption increases
For debtors consumption decreases as the interest repayments are higher.
THIRD AND EXTRA INCOME EFFECT FROM PROFIT.
As r0 is higher debt is more costly for firms so investment decreases and hence profits which decreases incomes
