1. Econ 202
Lecture 3
Goods market or Loanable-funds market equilibrium of a closed economy in the long run
(2)

2. In previous lectures, we have seen that
(a) for a closed economy, GDP is measured by
Y = C + I + G
(b) national saving in an economy is given by
S = Y – C – G
and,
(c ) since Y = C + I + G can be written as Y – C – G = I, and S = Y – C – G,
S = I

3. Notice that the equations Y = C + I + G and S = I hold
either with actual expenditures and desired production observed at the end of a period (then the equations hold automatically, that is, at the end of every period),
or with desired (or planned) expenditures and desired (or planned) production (then the equations hold only if the desired expenditures and desired production are consistent with each other, in which case we talk about “equilibrium”).
And if the desired expenditures and desired production are not consistent with each other (if there is “disequilibrium”), then some desired expenditures will not be able to be realized, and either Y or r or both will have to change.

4. That's why we study (changes in) equilibrium in the goods market or in the loanable funds market: To understand / explain / predict changes in Y or r.
We do this by focusing on equilibrium conditions like
desired Y = desired C + desired I + desired G
(goods market equilibrium) or
desided S = desired I
(loanable funds market equilibrium)

5. As we do such analysis by using the loanable funds market equilibrium condition, for example, we have to consider what desired S and desired I separately depend on.
This requires that we consider first what desired C depends on.

6. Factors that affect desired C
These are the main factors that affect desired C:
Real interest rate, r (–)
Current disposable income, YD (+)
where YD = Y – T
Expected future disposable income, YDfe ... (+)
where YDfe = Yfe – Tfe
Wealth, Ω (+)
...

7. In other words, desired consumption expenditures C depends on r, Y, T, Yfe, Tfe, Ω, … .
We could express this idea by using mathematical language and saying that C is a function of r, Y, T, Yfe, Tfe, Ω, … or by writing
C = C( r, Y – T, Yfe – Tfe, Ω, …)
(–) (+) (+) (+)
where C(.) on the righthand side is called the “consumption function”.

8. Marginal propensity to consume out of current disposable income
The dependence of C on other factors exhibits (or, the consumption function has) an interesting property:
As YD increases and, as a result of this, C increases also, the increase in C will be less than the increase in YD, or ΔC < ΔYD, or
ΔC / ΔYD < 1.
The ratio ΔC / ΔYD is called MPC (the “marginal propensity to consume” out of current disposable income).
MPC is (approximately) the slope of the consumption function as C is plotted against YD.

9. Since YD = Y – T, we can express the change in C as follows:
ΔC = MPC ΔYD
ΔC = MPC (ΔY – ΔT)

10. Factors that affect desired S
Since S = Y – C – G and C depends on r, Y, T, Yfe, Tfe, Ω, … , it follows that desired S depends on the following factors:
Real interest rate, r
Current real GDP, Y
Current taxes, T
Government purchases of goods and services, G
Expected future GDP, Yfe
Expected future taxes, Tfe
Wealth, Ω

11. We can designate the dependence of desired saving S on the factors listed above as the “saving function”.
We are now ready to draw the graph of the saving function.

12. Desired saving
Interest rate, r S
Saving, S, Investment, I

13. S curve is drawn for any given set of values of Y, T, G, Yfe, Tfe, Ω, ...
Interest rate, r
S (Y, T, G, Yfe, Tfe, Ω, ...)
Saving, S, Investment, I

14. S increases at any r as Y increases
Interest rate, r
S (Y1, T, G, Yfe, Tfe, Ω, ...)
S (Y2, T, G, Yfe, Tfe, Ω, ...)
Saving, S, Investment, I

15. Factors that affect desired I
These are the main factors that affect desired I:
Real interest rate, r … (–)
Expected future profitability of new capital investments
(expressed as “expected future marginal product of capital” and denoted by MPKfe) … (+)
Expected future tax rates, τfe … (–)
(future tax rates that are expected to be applied to profit income)
...

16. Desired investment
Interest rate, r I
Saving, S, Investment, I

17. I curve is drawn for any given set of values of MPKfe, τfe, ...
Interest rate, r
I (MPKfe, τfe, ...)
Saving, S, Investment, I

18. I increases at any r as MPKfe increases
Interest rate, r
I (MPKfe2, τfe, ...)
I (MPKfe1, τfe, ...)
Saving, S, Investment, I

19. Equilibrium Interest rate, r S (Y, T, G, Yfe, Tfe, Ω, ...) equi r
I (MPKfe, τfe, ...)
equi S Saving, S, Investment, I
= equi I

20. Question:
What are the exogenous factors in the above analysis / model?
What are the endogenous ones?

21. What happens if one of the exogenous factors changes?
Suppose, for example, the government increases its purchases of goods and services (say, from G1 to G2) and keeps it constant at the new level, (that is, at G2).
What happens in the goods (or, loanable-funds) market?
We know from our discussion before that an increase in G causes S to decrease at any r so that S curve shifts left.

22. Change in Equilibrium: G increases
Interest rate, r S (Y, T, G2, Yfe, Tfe, Ω, ...)
S (Y, T, G1, Yfe, Tfe, Ω, ...)
r E2
r E1
I (MPKfe, τfe, ...)
S S Saving, S, Investment, I
= I = I1

23. There are different possibilities as to how a new equilibrium will be reached.
Either, Y stays constant, and r increases (from r1 to r2). This is the new equilibrium at point E2. As a result of the increase in G, S and I decrease (to S2 and I2). Increased government purchases cause a decrease in private investment (“crowding out”).
Or, r stays constant, and Y increases (from Y1 to Y2). And as Y increases S increases again until it becomes equal to I at the initial r. This is the new equilibrium at point E1. Increased government purchases cause an increase in GDP.

24. Change in Equilibrium: G increases
Interest rate, r S (Y1, T, G2, Yfe, Tfe, Ω, ...)
S (Y1, T, G1, Yfe, Tfe, Ω, ...)
r E = S (Y2, T, G2, Yfe, Tfe, Ω, ...)
r E1
I (MPKfe, τfe, ...)
S S Saving, S, Investment, I
= I = I1

25. Long run equilibrium
If we consider a situation in which Y = YLR before G is increased and make the simplifying assumption that YLR will stay constant,
the equilibrium at point E2 in the above diagrams can be identified with the long run equilibrium of the economy and explains what essentially happens in the economy after G is increased:
After G is increased, r will be higher and I will be lower compared to what they would have been if G had not been increased.

26. It is an important simplification to assume that YLR will stay constant before and after G is increased and actual Y stays at (or returns to) YLR
because, in order that Y return to YLR, prices and wages must have adjusted to the new market conditions after G has been increased, and this takes some time due to the fact that prices and wages change slowly rather than instantly.
Then, since time will have passed and physical capital stock K and population (and amount of labor available for work) will have grown during that time, YLR will have grown also (and not have remained constant).

27. Alternatively, we could do a more complicated analysis by allowing time to pass before prices and wages change and actual real GDP (Y) returns to long run GDP (YLR), and letting YLR not stay constant during that time but to grow.
But the essential conclusion from such an analysis would not be different from our conclusion above, which was:
After G is increased, r will be higher and I will be lower compared to what they would have been if G had not been increased.

28. Change in Equilibrium: MPKfe increases
Interest rate, r
S (Y, T, G, Yfe, Tfe, Ω, ...)
r E2
r E E3
I (MPKfe2, τfe, ...)
I (MPKfe1, τfe, ...)
S1 S Saving, S, Investment, I
= I1 = I2

29. Why does G affect S, and by how much under what circumstances?
Let us try to understand why S changes as G changes, and by how much does it change under what different circumstances.
When G is increased, T can also be increased or not.
If T is not increased, the government will have a budget deficit, and the deficit has to be covered by new borrowing.
If the government borrows more from people, it will have to increase taxes sooner or later, so future taxes (Tf) increase.
And if Tf will have to be increased, people may not expect this (so Tfe = constant) or they may anticipate it (so Tfe increases also).

30. Effect of an increase in G (T increased also)
First, suppose G is increased together with an increase in T so that ΔT = ΔG. Then,
S = Y – C – G
ΔS = ΔY – ΔC – ΔG
ΔS = ΔY – MPC (ΔY – ΔT) – ΔG
ΔS = 0 – MPC(0 – ΔG) – ΔG
ΔS = – (1 – MPC) ΔG
S decreases at any r by (1 – MPC) ΔG.

31. Effect of an increase in G (T increased also)
Interest rate, r S (Y, T + ΔT, G + ΔG, Yfe, Tfe, Ω, ...)
S (Y, T, G, Yfe, Tfe, Ω, ...) r2 r1
I (MPKfe, τfe, ...)
Saving, S, Investment, I
(1 – MPC) ΔG

32. Effect of an increase in G (T constant)
Second, suppose G is increased but T is kept constant. Furthermore, people do not anticipate any changes in future taxes, so Tfe = constant,
which means that expected future disposable income does not change, so YDfe = constant.
Therefore, none of the factors that affect C changes, so C = constant also. Then,
S = Y – C – G
ΔS = ΔY – ΔC – ΔG
ΔS = 0 – 0 – ΔG = – ΔG
S decreases at any r by ΔG.

33. Effect of an increase in G (T constant)
Interest rate, r S (Y, T, G + ΔG, Yfe, Tfe, Ω, ...)
S (Y, T, G, Yfe, Tfe, Ω, ...) r2 r1
I (MPKfe, τfe, ...)
Saving, S, Investment, I ΔG

34. Third, think about the following question:
Suppose G is increased but T is kept constant, AND people do anticipate that the government will have to raise taxes sooner or later, so Tfe increases also. What is the effect of an increase in G on the S curve under these circumstances?

35. Why does T affect S, and by how much under what circumstances?
Suppose current taxes are reduced without changing G.
When T is decreased but G is not decreased, the government will have a budget deficit, and it has to be covered by new borrowing.
If the government borrows more from people, it will have to increase taxes sooner or later, so Tf increases.
And if Tf will have to be increased, people may not expect this (so Tfe = constant) or they may anticipate it (so Tfe increases also).

36. Effect of a decrease in T
Suppose current taxes are decreased by a certain amount ΔT, so that T changes to T + ΔT, with ΔT < 0, but government purchases are kept the same, so G = constant. Furthermore, people do not anticipate any changes in Tf, so Tfe = constant. Then,
S = Y – C – G
ΔS = ΔY – ΔC – ΔG
ΔS = ΔY – MPC(ΔY – ΔT) – ΔG
ΔS = 0 – MPC (0 – ΔT) – 0
ΔS = MPC ΔT
S changes at any r by MPC ΔT, a decrease since ΔT < 0.

37. Effect of a decrease in T
Interest rate, r S (Y, T + ΔT, G, Yfe, Tfe, Ω, ...)
S (Y, T, G, Yfe, Tfe, Ω, ...) r2 r1
I (MPKfe, τfe, ...)
Saving, S, Investment, I
– MPC ΔT