9. Producer strategies | 13 Sept 1999 |
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 producers | Equations | 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), people | X(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/year | X(2) = U(5) <= whDay/whNom * X(1) | Eq. 9.1:4 replaces Eq. 5.1:4 |
Table 9.1:2. Producer free 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 equation | Eq. 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 equation | Eq. 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.
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.
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.
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