6. Household free strategies 07 October 1999

To Chapter 5

  1. Free strategies.
  2. Consumption limitation.
  3. Reference case for simulations
  4. Inelastic demand
  5. Elastic demand
  6. Desired saving strategy
  7. Exercises.
  8. References.

6.1 Free strategies

The possible free household strategies are one of the following:

Flow decided by householdsEquation Eq. no
Goods and services, X(7), pmy/year X(7) = U(1)Eq. 6.1:1
Expenditures, X(9), CU/yearX(9) = U(1) Eq. 6.1:2
Savings, X(10), CU/yearX(10) = U(1) Eq. 6.1:3

Table 6.1:1. Household free strategies.

There is a single decision variable U(1) because only one variable can be decided about. U(1) has a different meaning in each case. U(1) can have different values from time to time.

6.2 Consumption limitation

A limit on the consumption volume can be added to all strategies. That is that the stocks at the end of a period can not be less than zero. If the result of any strategy is that there is a deficit in stocks at the end of the period, then the strategy equation has to be replaced by equation Eq. 4.1:12 from the previous chapter.

LimitationEquation Eq. no
Stocks are zero at the end of the period Y(3)(t+Dt) = Y(3)(t) + X(6)*Dt = 0 or
X(6)*Dt = - Y(3)(t)
Eq. 6.2:1

Table 6.2:1. Limitation on household strategies.

The flow out of the stocks is just as big as to exactly empty the stocks at the end of the period.

6.3 Reference case for simulations

A case with steady state is chosen as reference case. Investments exactly balance the consumption of fixed capital (the wear of machinery and buildings). No stocks are accumulated or retracted, which means that the sum of the consumption and investment flows equals the total production. The total production is determined from the amount of fixed capital, Y(2), and the daily working hours. The amount of fixed capital also determines the number of employees. The productivity factor is one (=1).

The household strategy is to keep to constant consumption, inelastic demand curve. The producer strategy is to stick to constant dividends and to make no change in stocks. All dynamic behavior of this model comes from change in fixed capital and stocks, which were held constant so nothing changes with time. The payment flows simply reflect the real flows through price and wage levels.

Figure 6.3:1 Real flows of reference case

Figure 6.3:2 Payment flows of reference case

6.4 Inelastic demand

Suppose that the households want to consume a little more than before, they increase their consumption from 80 pmy/year to 81 pmy/year. The price of the goods and services is 1.25 CU/pmy, so the expenditures increase from 100 CU/year to 101.25 CU/year. Because they can not influence their incomes, they have to decrease the saving from 10 CU/year to 8.75 CU/year.

The producer strategy is, as before, to keep the dividends constant = 10 CU/year. This makes it necessary to sacrifice the investments which will change from 25 CU/year (20 pmy/year) to 23.75 CU/year (19 pmy/year). The increase of the consumption by 1 pmy/year is taken from the investments flow. Now the investments can not keep up with the wear of fixed capital so the production capacity will diminish. The situation is shown in figures 6.4:1 and 6.4:2 below.

Figure 6.4:1 Real flows with fixed private consumption.

Figure 6.4:2 Payment flows with fixed private consumption.

Bold figures show the flows just after the households have decided to increase their consumption. The first changes in payment flows occur only in the expenditure (+1 CU/year), investment (-1 CU/year) and saving flows (-1 CU/year). These three flows form a loop as indicated by heavy lines in the figure. A flow of 1 CU/year is superimposed clockwise on the original flows.

Red figures show the situation after 3 years. The volume of fixed capital has decreased from 100 pmy to 92 pmy. As the employment factor of the fixed capital is 1 person/pmy, the number of people employed is now 92. These people can produce 92 pmy/year of commodities which have to be shared between private consumption (81 pmy/year) and investments (11 pmy/year). The production capacity rapidly decreases as shown in figure 6.4:3 below.

Figure 6.4:3 Development of investments and fixed capital.
The calculation has been done without considering the limitation that investments have to be positive as well as the amount of fixed capital can not be negative. That means that the dynamic behavior is exaggerated. However, it clearly shows how unstable the economy is. The collapse occurs in the year 2001 when no more commodities can be produced.

This rarely happens in a real economy. What stabilizing mechanisms help to save the situation? There are three candidates for cures: The households decrease their consumption because of less incomes, the producers accept less dividends and invest instead or increase prices to finance more investments.

Figure 6.4:4 Development of investments and fixed capital when private consumption has decreased to 79 pmy/year at beginning of year 1996.

Less household consumption, (81->79 pmy/year) after one year makes it possible to increase investments again. No the system in unstable in the other direction, the production explodes after some time.

Higher prices do not help, unless the consumption is decreased. Higher prices only lead to less saving, which in turn gives less investments and less production capacity. Nor do lower prices help. The key is still lower consumption and lower prices will definitely not lead to that goal. Lower dividends have the same effect as higher prices, consumption is still too high.

The conclusion is that financial measures do not work unless the real economy is affected. The strategy chosen by the households was equivalent to a completely inelastic demand curve. A more realistic household strategy that automatically adjusts for prices may help.

6.5 Elastic demand

If the households decide to spend a certain amount of money on private consumption, the we get a demand curve with elasticity = 1. One percent higher prices (CU/pmy) give one percent less consumtion (pmy/year).

We assume as before that the households increase their consumption from 80 pmy/year to 81 pmy/year. In terms of expenditures, this corresponds to an increase from 100 CU/year to 101.25 CU/year. The initial behavior of the economy is the same as before, there are not enough resources to reinvest in fixed capital so production capacity decreases. Now we increase the prices from 1.25 CU/pmy to 1.28 CU/pmy after one year (beginning of year 1996). The consumption decreases from 81 pmy/year to 79.1 pmy/year and we get almost exactly the same development of investments as in figure 5.6:4 above. The consumption and production looks like in figure 6.5:1 below.

Figure 6.5:1 Development of production and consumtion when private prices have increased to 101 CU/year at beginning of year 1996.
The difference between the production curve and the consumption curve is what remains for investments. When consumption decreases in year 1996, enough investments can be made for reinvestments and a slight increase of fixed capital. The investment increase very rapidly after some years and the economy will explode if no actions are taken. One measure would be to relax consumption, e.g. by decreasing prices. The households may also decide to spend more because of higher collective incomes. The production increase has made it necessary to employ more people. The total incomes have increased correspondingly, see figure 6.5:2 below:

Figure 6.5:2 Household wages and expenditures.

6.6 Desired saving strategy

A third household strategy is to look on the difference between incomes and expenditures. This is to amount that can be saved. Suppose that the households want to have some margin for future needs and that they do not want to or can not borrow money for current expenditures. We test this strategy by starting with the same conditions as before. In this case the households decide to buy more commodities but set the goal in terms of saving. The saving is decreased from 10 CU/year to 8.75 CU/year.

Figure 6.6:1 Investments when saving less.

Investments are still lower than the wear of fixed capital so the production capacity continues to decrease. The difference is now that the private consumption also decreases and leaves more resources for investments.

Figure 6.6:2 production and consumption when saving less.

We try to increase the prices this time too. The price increase is the same as before, from 1.25 CU/pmy to 1.28 CU/pmy after one year (beginning of year 1996). More expensive commodities make the households to consume less and investments increase again.

Figure 6.6:3 Investments when saving less but with higher prices.

As more fixed capital is accumulated, the production and consumption can increase again. Note the it is the total consumption that increases, the consumption per capita is less than before because of the higher price and that wages have not changed.

Figure 6.6:4 Production and consumption when saving less but with higher prices.

Suppose that the households want to save more when the production increases. Saving is increased from 8.75 CU/year to 11.25 CU/year in the beginning of year 1997.

Figure 6.6.5 Production and consumption when saving more from year 1997.

The initial sacrifice is less consumption but in the long run production and consumption will be higher than before. The thin solid lines show the same case as in figure 6.6:4. The illustrates the old wisdom that the society has to save and invest to get economic growth.

The desired saving strategy reacts to changes in both incomes and expenditures. It seems to be more stable and also more realistic than the other strategies, desired consumption and desired expenditure.

6.7 Exercises

I will try to add some exercises to each chapter. I do not publish any answers at the moment but readers are welcome with their suggestions to my e-mail. If the reader wishes, I can add the answers to this document. I reserve the right to add my own comments to the answers. If contributors wish, I can also, as far as I have time, return personal comments by e-mail.  

6.8 References

  1. Ref.1

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