Economists at positive deposit

With money on the club account, economists yield a revenue of the reposit. The interest rate is dependent on the number of economists, and can be described as: [interest rate] = SQRT(X)*0,0375%, where X denotes the number of economists. Further the interest reduction is rounded down to the nearest multiple of 100 (EUR)

The weekly net revenue (neglecting the cost of 1800 to fire the economist) can be depicted as a function of resposit and economists as in fig. 1 below.

The graph indicates, that you need a reposit of at least 5'066'666,7 to make a positive net revenue from an economist. The optimum number of economists (i.e the amount where the net revenue is maximized) is opviously dependent on the team reposit. The optimum number is sketched in tabel 1. As the maximum interest is 25000 EUR it can be seen, that the optimum number of economists will start falling with the reposit size after a given point. This also means, that it is NEVER reasonable to hire more than 7 economists.

The maximum net revenue is depicted in fig. 2 as function of reposit. Obviously the revenue is relative very low compared to the reposit. Actually the highest possible weekly net revenue is 23'200 (reached when reposit is more then 66'666'667).

Notice, that the cost of 1800 EUR when the economist is fired is NOT included in the calculations. This will impact the optimum choice if the resposit (or part of it) is spend a few weeks after the hiring. E.g. one economist and a reposit of 5'066'666,7 gives a weekly net revenue of 100 EUR. Thus, assuming that the reposit is (approximately) constant, you need to keep the economist for more than 18 weeks before the net revenue (incl. the firing cost) is actually positive. If you expect to collect money through several seasen, it is optimum to hire economists in the week, where the limit to the next interval is passed (with refernence to table 1).

Economists at negative deposit

With a negative reposit, an economist reduces the interest to be paid. Without economists the weekly interest rate is 3.33%. With economists the rate can be reduced with 20%*SQRT(X), where X denotes the number of economists. Further the interest is rounded down to the nearest multiple of 100 (EUR)

Considering a single week, the first economist will earn his own wage at a debt of 1800/(3,33%*20%) = 270'000 EUR. To actually make a positive weekly net revenue of the economist, the debt should be at least 285'000 EUR - this will give a weekly net revenue of 100 EUR. Including the cost to fire the economist, it is impossible to make a revenue by hiring an economist in a single week, since the economist will not give any reduction on the interests related to the debt larger than 500K EUR. Thus, the economist should be hired for several weeks, before it (theroetically) is recommendable to hire him. E.g. with a debt of 315'000 over six weeks, an economist will earn his own wage incl. firing cost providing a break-even point. The revenue of economists when in debt, are generally too small to actually make it worth considering. My recommendation is not to hire them.

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