Thus it can be seen that the difference in the Discretionary Profit and the Discretionary investment arises because of the amount of managerial slack. This can be represented by the given equation  where Π"D" is the discretionary profit, "I""D" is the Discretionary investment and "M" is the management slack. For simple representation of the model the managerial slack is considered to be zero. Thus there is no difference between the actual profit and reported profit, which implies that the discretionary profit is equal to the discretionary investment. I.e.  where Π"r" is the reported profit, Π is the actual profit, Π"D" is the discretionary profit and "I""D" is the discretionary investment. Such that the utility function of the manager becomes  where S is the staff expenditure and ID is the discretionary investment. There is a trade off between these two variables. Increase in either will give the manager a higher level of satisfaction. At any point of time the amount of both these variables combined is the same, therefore an increase in one would automatically require a decrease in the other. The manager therefore has to make a choice of the correct combination of these two variables to attain a certain level of desired utility. Substituting  The relationship between the two variables in the manager’s utility function is determined by the profit function. Profit of a firm is dependent on the demand and cost conditions. Given the cost conditions the demand is dependent of the price, staff expenditures and the market condition. Price and market condition is assumed to be given exogenously at equilibrium. Thus the profit of the firm becomes dependent on the staff expenditure which can be written as  Discretionary profit can be rewritten as  In the model, the managers would try to maximise their utility given the profit constraint  Fig 1. shows the various levels of utility ("U"1, "U"2, "U"3) derived by the manager by combining different amounts of discretionary profits and staff expenditure. Higher the indifference curve, higher is the level of utility derived by the manager. Hence the manager would try to be on the highest level of indifference curve possible given the constraints. Staff expenditure is plotted on the "x"-axis and discretionary profits on the "y"-axis. The discretionary profit in this simplified model is equal to the discretionary investment. The indifference curves are downward sloping and convex to the origin. This shows diminishing marginal rate of substitution of staff expenditure for discretionary profits. The curves are asymptotic in nature which implies that at any point of time and under any given circumstance the manager will choose positive amounts of both discretionary profits and staff expenditure.