Williamson’s Model of Managerial Discretion

2 years ago

Atiqur Rahman

15 minutes

Introduction

Williamson’s Model of Managerial Discretion was developed by Oliver E. Williamson in 1964. Williamson, like other managerial theories of the firm, assumes that utility maximization is the sole objective of the managers of a joint-stock organization. It is also known as the “Managerial Discretion Theory”.

Williamson emphasizes that managers are motivated by their own self-interest, and they try to maximize their own utility function. Alike Baumol’s sales maximization model, the utility maximization objective of the managers is subject to the constraint that after-tax profits are large enough to pay dividends to the shareholders.

However, it is pointed out that utility maximization by self-interest-seeking managers is possible only in the corporate form of the business organization, as there exists a separation of ownership and control.

This is basically the principal-agent problem. It explains the relationship between the principal (owner) and the agent (who performs the owner’s work). The principal-agent shows that whenever the difference between ownership and control exists, then the self-interest of the agent makes profits lower than in a situation where principals act as their own agents.

Williamson’s Theory of Managerial Discretion

Profit works as a limit to the manager’s utility maximization as the shareholders require a minimum profit to be paid out in the form of dividends. If these minimum profits are not covered, then the job security of the managers is put in danger. But, the managers are able to hold a powerful position if:

(i) the firm is showing a reasonable rate of growth,
(ii) minimum dividends are paid to the shareholders and
(iii) profits at any time are at an acceptable level.

Here the manager’s decision on price and output differs from the manager’s decision on price and output of a profit maximization firm.

Assumptions of Williamson’s Model Managerial Discretion:

(i) Imperfect Competition
(ii) Separation of Ownership and management.
(iii) A minimum profit to be able to pay to the shareholders.

The Factors that affect the Interest of Self-seeking Managers are:

a. Salary and other forms of Monetary Compensation
b. Management Slack or Non-essential Management Perquisites
c. Number of Staff under the Control of a Manager
d. The magnitude of Discretionary Investment expenditure by the Manager.

a. Salary and other forms of Monetary Compensation:

Salary and other forms of monetary compensation are one of the most important factors in determining the utility of managers. The higher the income the managers receive, the better their standard of living and status. So, the higher the salary and other monetary compensation and perks, the higher the utility of the managers.

b. Management Slack or Non-essential Management Perquisites:

The second factor that determines the utility of the managers is the amount of management slack. The management slack consists of non-essential management perquisites such as a well-furnished office, luxurious cars, entertainment expenses etc. These perks are giving them an incentive to the managers to enhance their status and prestige in the organization, which in turn contributes to the efficiency of the firm’s operation. These non-essential perquisites are also part of the cost of production of the firm.

c. Number of Staff under the Control of a Manager:

The third factor that determines the utility of the managers is the number of staff under the control of a manager. The greater the number of staff under the control of a manager, the more powerful is the manager. More staff under the manager enhances his status and prestige. According to Williamson, there exists a positive relationship between the number of staff and the salary of the managers. In the utility maximization model of Williamson, he used a single variable for the number of staff and salary of the managers as “monetary expenditure on the staff”.

d. Magnitude of Discretionary Investment expenditure by the Manager:

The fourth important factor that determines the utility of the managers is the magnitude of discretionary investment expenditure by the manager. The discretionary investment refers to the number of resources left at a manager’s disposal to be able to spend at his own discretion. This enhances his status and prestige in the organization. Here, the discretionary investment by the managers does not include those investment expenditures that are necessary for the survival of the firm. The discretionary investment by the manager includes spending on furniture, the latest equipment, decoration material etc.

Williamson’s Utility Function

The managerial utility function includes variables such as salary, status, prestige, job security and other monetary compensation. Out of these, salary is the only quantitative variable which is measurable. On the other hand, all other variables except salary are non-quantifiable, i.e. not measurable.

In the utility maximization model of Williamson, he used a single variable for the number of staff and salary of the managers as “monetary expenditure on the staff”. The utility function of managers is a function of salary, monetary expenditure on the staff and discretionary investment.

𝑈 = 𝑓₁(𝑆, 𝑀, 𝐼_𝐷)

Where,

U is utility

S is monetary expenditure on the staff

M is the management slack.

𝐼_𝐷 is a discretionary investment.

Here, the variables expenditure on staff salary, management slack and discretionary investment is used the unquantifiable concepts like power, status, job security, dominance etc. The variable expenditure on staff, management slack and disinvestment can be assigned some nominal values.

There exists a positive relationship between decision variables (S, M and 𝐼_𝐷 ) and utility. Any increase in the decision variables increases the utility of the managers. But the firm always chooses their values subject to the constraint, S≥0 and D≥0. Williamson also assumes that the law of diminishing marginal utility applies so that when additions are made to each of the decision variables S, M and 𝐼_𝐷, they yield smaller increments to the utility to the manager.

The demand curve faced by the firm is downward sloping:

Under Williamson’s model, the demand curve faced by the firm is downward sloping. The demand function can be written as:

Q = 𝑓₂ (P, S, Ɛ)

P = 𝑓₃ (Q, S, Ɛ)

Where,

Q is output

P is price

S is staff expenditure

Ɛ the demand-shift parameter reflects autonomous changes in demand

The demand curve is negatively sloped, implying that price and quantity have a negative relationship. i.e., ^𝜕𝑃/_𝜕𝑄 < 0.

When the prices increase, the quantity decreases, and when the price decreases, the quantity increases. It is also assumed that demand is positively related to staff expenditure and to the demand shift parameter ε. Thus,

𝜕𝑃/𝜕𝑆 > 0 𝑎𝑛𝑑 𝜕𝑃/𝜕Ɛ > 0

Any increase in staff spending causes an upward shift in the demand curve, allowing for a higher price to be charged. Any other change in the demand shift parameter that causes the demand curve to shift upward has the same effect. It could be an increase in income, a shift in taste in favour of a product, or something else.

Cost of Production:

The total cost of production is assumed to be an increasing function of output. This can be expressed as:

C = 𝑓₄ (Q)

Where,

C is cost

Q is output

The total cost increases with the increase in the level of output, i.e. ^𝜕𝐶/_𝜕𝑄 > 0.

Concept of Profit in the Williamson’s Model:

The various concepts of profit used in the Williamson model need to be understood clearly before moving to the main model. Williamson has put forth four main concepts of profits. These are actual profit, discretionary profit, reported profit and minimum profit.

(i) Actual profit (π):

The actual profit is defined as the revenue from sales less the production costs and the staff expenditure.

π = R – C – S

Where,

R is revenue,

C is the cost of production and

S is the staff expenditure.

(ii) Reported Profit (π_R):

This is the profit reported to the tax authorities. Reported profit (πR) is the difference between actual profits and supplementary or nonessential managerial emoluments as represented by the management slack. It is the actual profit minus the managerial emoluments (M), which are tax-deductible. So,

π_R = π – M = R – C – S – M

(iii) Minimum Profit (π₀):

Minimum profit (π₀) is the number of profits (after tax) which is required to be paid as an acceptable dividend to the shareholders of the firm. Suppose the shareholders do not get reasonable dividends. In that case, they may sell their shares and thereby expose the firm to the risk of being taken over by others, or alternatively, they will vote for a change of top management. Both of these actions by the shareholders will reduce the job security of the top managerial team.

Hence, some minimum profits should be earned by the manager for the shareholders in the form of dividends to keep them satisfied. Through this, he can ensure his job safety. To meet this objective, the reported profits must be at least as high as the minimum profit (π0) plus the tax (T) that must be paid to the government. This is mathematically expressed as:

π_R ≥ π₀ + T

The tax function is of the form T = Ť + t. π_R

Where,

t is the marginal tax rate or unit profit tax and

Ť is the lump-sum tax.

(iv) Discretionary profit (π_D):

Discretionary profit is the amount of profit left after subtracting from the actual profit (π), the minimum profit requirement (π0) and the tax (T). It can be expressed as:

π_D = π – π₀ – T

(v) Discretionary Investment (I_D):

Discretionary investment is the amount left from the reported profit after subtracting the minimum profit (π0) and the tax (T). It can be expressed as:

I_D = π_R – π₀ – T

Discretionary profit is different from discretionary investment. Discretionary profits are the amount left after minimum profit (π₀) and tax (T) are deducted from actual profits (π_D = π – π₀ – T) but discretionary investment equals the amount left from the reported profit after subtracting the minimum profit (π₀) and the tax (T). Thus, we have discretionary investment

I_D = π_R – π₀ – T

Since the difference between reported profits (πR) and actual profits (π) arises due to management slack and discretionary profits. It can be written as πD = ID + Amount of management slack. Thus, if management slack is zero, then

π_R = π and π_D = I_D

Simplified Model of Williamson’s Managerial Discretion

Under Willaimson’s model, the objective is the maximisation of the utility function subject to the minimum profit constraint. The minimum profit should be such that it is sufficient to pay satisfactory profit to shareholders and pay for necessary investments. Here we are taking a simple case where there is no management slack, i.e. M=0.

Objective Max U = f (S, 𝐼_𝐷)

Subject to π ≥ π₀ + T

As there is no management slack, so the discretionary investment absorbs all the discretionary profit. Thus the managerial utility function can be written as-

U = f [S, ( π – π₀ + T)]

Here, we are also assuming that there is no lump sum tax, i.e. Ť=0, so that T=t π. Thus,

U = f [S, (1 – t) π – π₀ ]

Where (1-t)π – π₀ is the discretionary profit π_D.

Graphical Representation of the Williamson’s Model:

The graphical representation of the equilibrium of the firm requires the construction of the indifference curves map of managers and the profit curve. An indifference map is a family of indifference curves. An indifference curve is a curve which shows different combinations of two goods yielding the same level of satisfaction to the consumer.

In other words, it identifies the various combinations of goods among which the consumer is indifferent. Here, the indifference curve under the Williamson model shows the relationship between monetary expenditure on the staff and discretionary investment. These are the two variables that determine the utility function of the managers.

The indifference curve is shown in the figure where staff expenditure (S) is measured on the x-axis and discretionary profit (πD) on the y-axis. Each indifference curve shows various combinations of staff expenditure (S) and discretionary profit (πD), which give the same level of satisfaction to the managers.

Consider the Figure below:

It is assumed that the indifference curves of managers are of well behaved:

Indifference curves are downward sloping.
They are convex to the origin, implying a diminishing marginal rate of substitution of staff expenditure and discretionary profit.
Two indifference families of indifference curves can never intersect each other.
The higher the indifference curve higher is the level of satisfaction.
The indifference curves do not intersect the axes.

The indifference curves do not intersect the axes. This is a very important property and needs to be explained properly. We have seen that expenditure on staff and discretionary profit are positively related to the utility function of the managers.

Any increase in expenditure on staff or discretionary profit or in both results in an increase in the satisfaction of the managers by increasing the utility. This assumption restricts the choice of managers to positive levels of both staff expenditures and discretionary profits, implying that the firm will choose values of π_D and S ‘that will yield positive utility.

It is shown in the figure below. Suppose the indifference curve does not intersect the axes. In that case, the model excludes the corner solutions, such as points A, B, C, D etc., where discretionary profit (π_D) would be zero in the final equilibrium of the firm.

We have derived the indifference curve of the managers and have seen that they are well-behaved. Now let us determine the profit function and then the equilibrium analysis of the firm. The relationship between S, staff expenditure, and π_D, discretionary profit, is determined by the profit function.

The profit function explains the relationship between profit and output. We have seen that output is a function of the price of the product, expenditure on staff and the demand shift parameter. Thus, the profit function is a function of the price of the product, expenditure on staff and the demand shift parameter

π = ƒ(Q) = f(P, S, Ɛ)

Where,

π is profit,

Q is output

P is price

S is expenditure on staff

Ɛ demand-shift parameter reflecting autonomous changes in demand

The profit function which explains the relationship between π₀ and S is shown below in the Figure below:

We can see from the figure that the profit curve initially rises, reaches a maximum and then falls thereafter as the level of production increases. It starts increasing from point a, reaches the maximum at point b and then starts falling and becomes negative after reaching point c. So, initially, both discretionary profits and staff expenditures increase with the level of production.

This increase continues till the maximum point on the profit curve. Beyond point b, where with the increase in production profit curve starts falling, and staff expenditures continue to increase. If these expenditures continue to increase and exceed point ‘c’, then the minimum profit constraint is not satisfied. So the region before point ‘a’ and to the right of ‘c’ are not feasible solutions.

It should be clear from the above discussion that the drawn profit curve does not include the minimum profit requirement π₀. Williamson’s model implies higher output, lower price and lower level of profit than the profit-maximization model.

Williamson’s Model of Managerial Discretion

Introduction

Williamson’s Theory of Managerial Discretion

Assumptions of Williamson’s Model Managerial Discretion:

The Factors that affect the Interest of Self-seeking Managers are:

a. Salary and other forms of Monetary Compensation:

b. Management Slack or Non-essential Management Perquisites:

c. Number of Staff under the Control of a Manager:

d. Magnitude of Discretionary Investment expenditure by the Manager:

Williamson’s Utility Function