INTRODUCTION The manager needs various techniques to assist and help him in making decisions that will ultimately maximise the value of the firm. These techniques and tools are quantitative in nature. The introduction of some commonly used tools used in managerial decision making becomes imperative.
In this unit we are going to discuss some basic techniques which would be helpful in understanding the concept of managerial economics, in turn helping us to apply these techniques as and when required.
OPPORTUNITY SET A set is a collection of distinct or well defined objects like (5, 6, 7) or (a, b, c). For example listing of all residents of Delhi or all animals in a zoo is difficult. Thus a set is also formed by developing a criterion for membership. For example the set of all positive numbers between 1 and 10 or set of all points lying on the line x + y = 4. In managerial economics the need is to define an opportunity set of a decision maker, i.e., the set of alternative actions which are feasible. For example, the opportunity set of a consumer is the set of all combinations of goods which the consumer can buy with his given income. Given the consumer’s budget and prices of all goods, the opportunity set is well defined, and we can find out whether the Five key functions of economics are represented graphically:
The “slope” in mathematical use is the concept of ‘marginalism’ in economic use. Thus if Y=Y(x), dy/dx stands for change in Y as a result of one unit change in X, i.e. marginal y of x. This slope or marginal function has enormous use in managerial economics. Thus,
In managerial economics, usually a function of several independent variables is encountered instead of a single variable case shown above. For example, a consumer’s demand for a product depends on the price of the product, price of other related goods, income, tastes, etc. When price changes, the effect on quantity demanded of the goods can be analysed only when all other variables are kept constant. The functional relationship that is obtained between the quantity demanded of a product and its own price is called a Partial Function (a function of one variable when all other variables are kept constant). The derivative of the partial functions are known as partial derivatives of the original function and is shown as df/dx1 or f1(x) or f’(x). The conventional symbol used in maths for the partial derivative is delta, d. Partial derivatives are functions of all variables entering into the original function f (x).
Optimisation is the act of choosing the best alternative out of the available ones. It describes how decisions or choices among alternatives are taken or should be made. All such optimisation problems have 3 elements:
a) Decision Variables: These are variables whose optimal values have to be determined. For example, a production manager wants to know at what level to set output in order to achieve maximum profit or maximum sales revenue. Here output is the decision or choice variable. Similarly labour, machine, time and raw materials are choice variables if a works manager wants to know what amount of these are to be used so as to produce a given output level at minimum cost. The quantity of any choice variable must be measurable (20kg, 5 labourers, 10 hours, etc.).
b) The Objective Function: It is a mathematical relationship between the choice variables and some variables whose values are to be maximised or minimised. For example, the objective function could relate profit to level of output or cost to amount of labour, machine, time, raw materials, etc. in the above example.
c) The Feasible Set: The available set of alternatives is called a feasible set. A solution to an optimisation problem is that set of values of the choice variables which is in the feasible set and which yields maximum or minimum of the objective function over the feasible set.