Week 4 - Production Economy

Question 1

What do firms do in period 1 and 2 in the production economy model?

Answer 1

In period 1 firms invest in physical capital which they use to produce goods in period 2

Question 2

What is the production function equal to and give an interpretation of the terms

Answer 2

Q2=A2F(I1), Production in period 2(Q2)= The firms investment in capital in period 1(F(I1), multiplied by the efficiency parameter A2

Question 3

What kind of function if F(I1), and what does this mean?

Answer 3

F(I1), is an increasing function meaning the more machines you buy the more production you have. It is also a concave function, meaning the additional production coming from an increase in investment is in decline.

Question 4

What is the MPK, and what is it equal to?

Answer 4

MPK, is the marginal product of capital and is the extra increase in output when capital stock is increased by one unit.

Question 5

What is the amount of debt in period 1 for firms equal to and give an explanation of this

Answer 5

Amount of debt in period 1 D1=I1, firms borrow money in period 1 to finance the purchases of investment goods so debt= investment goods

Question 6

What Is the firms profit in period 2?

Answer 6

Pie2=A2F(I1)-(1+r1)D1 or replace D1 with I1 as they are equal

Question 7

What is the optimal investment for firms

Answer 7

A2F’(I1)=(1+r1) this is when the marginal product of investment equals its marginal cost

Question 8

What Is the firms profit in period 1?

Answer 8

Pie1=A1F(Io)-(1+ro)Do

Question 9

What is the Budget constraint for households in period 1 and period 2?

Answer 9

• Period 1: C1+(B1h-B0h)= Pie1 +roBoh - Consumption + Households net asset = Profit in period 1 + NII generated
• Period 2: C2+(B2h-B1h) =Pie2 + r1B1h

Question 10

What do the optimality and transversality condition cause B2h to equal?

Answer 10

• Optimality condition B2h>0
• Transversality condition B2h≥0
• Hence B2h=0 Assets in period 2 should be 0 as you should spend

Question 11

What is an economies inter temporal resource constraint equal to?

Answer 11

C1 + C2/1+r1 +I1 = A2F(I0) + A2F(I1)/1+r1 +(1+ro)B*o

Question 12

What is the End of P1 net investment position equal to: B1= CA1 + Bo

Answer 12

B1= CA1 + Bo

Question 13

What is the current account in period 2 equal to?

Answer 13

CA2= TB2 + r1B*1

Question 14

What is national savings equal to?

Answer 14

S1= Q1 + roB*o - c1

Question 15

How do changes to the interest rate affect the model?

Answer 15

1. Substitution effect higher interest rate in period 1 leads to a lower consumption in period 1
2. Income effect: If household is a borrower (B2h<0) higher interest rate leads to lower c1 if household is a saver Boh>0 tiger r1 means a higher c1.
3. Assumption SE dominates YE