9. Producer strategies 13 Sept 1999

To Chapter 8

  1. Free strategies
  2. Model strategies
  3. Determination of wage level and daily working hours
  4. Simulations with linear model strategies
  5. Simulations with dynamic model strategies
  6. Simulations with non linear model strategies
  7. Exercises.
  8. References.

9.1 Free strategies

The free strategies can be expressed by two equations if the production capacities are fully used. Two additional equations can be defined if less is produced and will then replace the corresponding process equations.

Flows decided by producersEquations Eq. no
Investments, X(12), CU/year
Dividends, X(13), CU/year
X(12) = U(2)
X(13) = U(3)
Eq. 9.1:1a
Eq. 9.1:2a
Investments, X(4), pmy/year
Change in stocks, X(6), pmy/year
X(4) = U(2)
X(6) = U(3)
Eq. 9.1:1b
Eq. 9.1:2b
Change in stocks, X(6), pmy/year
Dividends, X(13), CU/year
X(6) = U(2)
X(13) = U(3)
Eq. 9.1:1c
Eq. 9.1:2c
Work force, X(1), peopleX(1) = U(4)
U(4) <= Y(1)
U(4) <= fWfCp * Y(2)(t)
Eq. 9.1:3
replaces Eq. 5.1:3
Work done, X(2), wmy/yearX(2) = U(5) <= whDay/whNom * X(1) Eq. 9.1:4
replaces Eq. 5.1:4

Table 9.1:2. Producer free strategies.

9.2 Model strategies

The producers may be interested to invest when the consumption is high or when the stocks are low. The investments can be in more capital of the same kind or in capital with higher productivity. The producers are free to pay the dividends that they choose but it is unlikely that they want to borrow money for paying dividends. The dividends can be assumed to be a fraction less than unity of the gross profits. The producers may borrow money to finance their investments. Let us make some model strategies based on these assumptions.

Assume that the producers want to keep the stocks at a certain level stoAim (pmy). When the stocks are low they invest so that they can reach that level within a time tiStoAim (years). The deficit of the stocks are then stoAim-Y(3) and the necessary flow to fill the stocks is (stoAim-Y(3))/tiStoAim. If the flow already is X(6), then the flow has to be increased by (stoAim-Y(3))/tiStoAim - X(6). If the productivity factor of the capital is fPdWk, the daily working hours whDay and the employment factor of the capital fWfCp, then a certain amount of fixed capital Y(2) is able to produce a product flow of fPdWk * whDay/whNom * fWfCp * Y(2). See equation Eq. 4.2:1 from chapter 4. An increment of the fixed capital by DY(2) during the time tiStoAim that gives the desired increase in production requires the investment flow X(4) is increased by DY(2)/ tiStoAim. We get the equations:

DX(6) = (stoAim-Y(3))/tiStoAim - X(6)(t-Dt) = fPdWk * whDay/whNom * fWfCp * DY(2)

DX(4) = X(4) - X(4)(t-Dt) = DY(2)/ tiStoAim or X(4) = X(4)(t-Dt) + DY(2)/ tiStoAim

Strategy equationEq. no
X(4) = X(4)(t-Dt) + [(stoAim-Y(3)(t- Dt))/tiStoAim - X(6)(t-Dt)] /
(fPdWk * whDay/whNom * fWfCp * tiStoAim)
Eq. 9.2:1

Table 9.2:1. Investments strategy for automatic adjustment to sales.

This model assumes that decisions are based on the past experience. The increased investments will draw resources from product flow, so the increase in stocks will not be as big as expected. The wear will also increase as the amount of fixed capital increases which in turn require more replacement investments. The investment plans will always be one period old. Of course, the equations can be formulated to include the new unknown flows X(5) and X(6) implicitly, but I judge that it is less realistic with such a forelooking strategy. A more realistic or elaborated investment plan will include cash flow and profit considerations and not only capacity considerations. It will also be combined with a informal (subjective) judgment of the future.

The owners of the companies want a return on their investments. The dividends can be set somewhat arbitrarily but legislation often restricts how much dividends may be paid. The own capital of the company has to be at least a certain fraction of the share capital. There are examples the dividends have been financed by selling new shares, e.g. the "pyramid" games in Albania during 1997. As this simple model does not keep track of how much of the household savings, flow X(10) in figure 5.5:1, that are invested in shares and how much is borrowed to the companies, it is not possible to make a very complicated model. Let us simply assume that the dividends, X(13), are a share of the gross profits, X(11). A additional restriction may be that the dividends always are positive. The companies never require dividends to be paid back. They may ask the owners for more money, but those money are included in the saving flow, X(10).

Strategy equationEq. no
X(13) - rDivGrPr * X(11) = 0; X(13) >= 0 Eq. 9.2:2

Table 9.2:2. Dividend model strategy.

We have now formulated strategies for investment and dividends. The investment strategy is dynamic in the sense that it uses flow (X(4), X(6)) and state variables (Y(3)) from the past. The dividend strategy is nonlinear because of the restriction to positive flows.


The product prices, pr, are set by the producers. The prices are set to cover the production costs and to give some profits. We will now only use a free strategy for prices. A more sophisticated strategy would consider how much the sales decrease with higher prices (price elasticity) and try to maximize the profits in the short or long run. Here, we will only investigate how the economy changes when prices are changed.

9.3 Determination of wage level and daily working hours

The wage level is set by both employees and employers in a bargaining process. The wages can often not be lowered, in Sweden, the agreements between trade unions and employers do not allow wages to be reduced. The wage level is in this model set by a free strategy.

9.4 Simulations with linear model strategies

9.5 Simulations with dynamic model strategies

9.6 Simulations with non linear model strategies

9.7 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.


9.8 References

  1. Ref 1

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