## FYBCOM Sem 1 Basic Tools in Economics Chapter 3 Notes 2024 – Functions

**FYBCOM Sem 1 Basic Tools in Economics Chapter 3 Notes** is Functions In this chapter Functions help economists model and analyse economic phenomena. A function describes a relationship involving one or more variables. It explains how changes in one variable affect another.

The notes we provide for FYBCOM students are not tied to a certain course. Students pursuing FYBAF and FYBMS study similar subjects in their first semester, such as Basic Economics Tools, so these notes are equally beneficial to them. Our detailed notes are meant to make it easier for all students in these courses to understand the important concepts. Whether you are in FYBCOM, FYBAF, or FYBMS, these notes will help you succeed academically.

**Q.1 A) Select the most appropriate alternative and rewrite the statement:**

1) What does a function describe in the context of economics ?

a) The relationship between two variables

b) **The impact of changes in one variable on another **

c) The total cost of production

d) The average revenue per unit sold

2) What does the functional notation Z=f(X) represent?

a) **The relationship between two variables**

b) The impact of a constant on changes in another variable

c) The marginal cost of production

(d) The average cost per unit sold

3) Y = a + bX + cX^{2 }is a/an

(a) Log-linear function

b) Cubic function

c) **Quadratic function**

d) Exponential function

4) In the function Y = f (X, ₹) € represents

a) the dependent variable

b) the omitted variable

c) the independent variable

d) **the error term**

5) A functional relation can be expressed

a) in words

b) in graphs

c) in mathematical equations

d) **as all of the above**

6) In the linear function the highest exponent of the variable is

a) 1

b) 2

c) 3

d) **none of the above**

7) In the case of the cubic total cost function the coefficient c is

a) **negative **

b) positive

c) zero

d) any of the above

8) z = a*b^{x }is a/an

a) Log-linear function

b) Cubic function

c) Quadratic function

d) **Exponential function**

9) Functions are important for

a) Describing economic relationships

b) Modelling economic phenomena

c) Making informed predictions

d) **All of the above**

10) Which one of the following is not a function in macroeconomic ?

a) Consumption function

b) **Cost function**

c) Investment function

d) Savings function

**Q.1 B) State whether the following statements are true or false.**

- A function expresses the independence of one variable on one or more other variables.
**– False** - Log linearisation is a technique to approximate linear equations with non-linear ones.
**– False** - The choice of symbols to designate different rules is not arbitrary so we cannot use any convenient symbols.
**– False** - Two steps are needed in order to express a functional relation in symbols.
**– True** - The variable on he left-hand side of a function is called the dependent variable.
**– True** - The variable on the right-hand side of a function is called the dependent variable.
**– False** - If we wished to talk about one particular term in a series without indicating which one, we would talk about the (i + 1)th term.
**– False** - When we say that functional relations are deterministic, these relations follow predictable patterns based on cause-and-effect relationships
**– True** - All the factors other than X that effect the measured value of Y are summarised by the error term. €.
**– True** - Exponential functions in economics represent the growth or decay of a variable at a constant percentage rate.
**– True**

### 1) What is the functions ? Explain a function as a role.

**Answer:** A functions is a mathematical concept that describes a relationship between variable, indicating how changes in one variable affect another. In economics, functions are used to model and analyze relationships among various economic factors. Specially, function expresses the dependance of one variable or more variables. For example, the function representing a students grade can be expressed as:

**Student’s Grade = (0.50 x study hours) + (0.25 x class attendance) + (0.25 x prior GPA)**

In this case, the student’s grade depends on study hours, class attendance, and prior GPA, with study time having grater impact than the factors

The role of a function can be articulated through **functional notation**, typically written as Y = f(X), Which means that Y is determined by applying a rule f to the variable X. This notation simplifies the representation of relationships and allows economists to express complex interactions in a manageable format.

**Functions as Roles **

1) Describing Relationship

2) Making Predictions

3) Simplifying Complex Interactions

4) Facilitating Optimization

5) Graphical Representation

### 2) What is the functions ? What steps should an economist follow to express a relationship in economics ?

**Answer:** A function expresses the dependence of one variable on one or other variables. It describes how changes in one variable affect another. These functions help economists model complex economic systems by expressing how one variable changes inn response to change in another.

**Steps for economists to express relationships:**

Identify Variables

Assign Symbols

Establish Functional Relationships

Use Functional Notation

Consider Additional Factors

### 3) What is the error term in functions ?

The functional relation considered above was deterministic^{2}, in the sense that, given the value of Y, we know the value of C exactly. Relations in economics are seldom of this sort, except where definitions are being expressed. When an economist says that the world behaves so that Y = f (X), he does not expect that knowing X will tell him exactly what Y will be, but only that it will tell him that Y will be within some margin of error.

The error in predicting Y from a knowledge of X arises for two quite disinct reasons.

1) First, there may be other variables that also affect Y. Although we may say that the quantity of butter demanded is a function of the price of butter, q,, = f (p},), we know that other factors will also influence this demand. A change in the price of margarine will certainly affect the demand for butter, even though the price of butter does not change. Thus, we do not expect to find a perfect relation between q_{b} and p_{b} that will allow us to predict g, exactly from a knowledge of p_{b}

2) Second, we can never measure our variables exactly, so that, even if X is the only cause of Y, our measurements will give various Ys corresponding to the same X. In the case of the demand for butter, our errors of measurement might not be so large.

In other cases, errors can be substantial. In the case of a relation between total spending on consumption goods and total income earned in the nation (C = f(Y)), our measurements of both C and Y may be subject to quite wide margins of errors.

We may thus observe various values of C associated the same measured value of Y, not because C is the varying independently of Y, but because our error of measurement itself varying from period to period.

### 4) What are the various types of functions in economics ?

In economics, various types of functions are commonly used to describe relationships between variables.

Let’s explore a few of them:

**Linear Function**: In the linear function each term contains at most one variable, and the exponent of the variable is 1. It may take the form f (x) = a + bx

Here, b represents the slope (rate of change the independent variable x or in other words the behavioural coefficient^{3}), and a is the vertical intercept [value of f (x) when x = 0]^{4}**Non – Linear Function**are more complex than linear functions

**The Quadratic Function:** The Quadratic Function contains a squared term (exponent 2) in addition to linear terms. it may take the form f (x) = a + bx + cx^{2} (where c ≠ 0)

If the coefficient c is positive the graph of the function is U’ shaped. An example of the quadratic function is the average cost function. If c is negative in the quadratic function above, the graph of the function is shaped like an inverted U. An example of such a function in economics would be the total revenue function.

**Cubic Function:** A cubic function always contains a cubed term; E.g., X^{3}. A general formula relating x to y as a cubic function is y = a + bx + cx^{2} + dx^{3}.

A common cubic function in economics is the total cost function, in which the coefficient c is negative. A cost function is specified as TC = a + bQ – cQ^{2} + dQ^{3}. It gives rise to an S shaped TC function.

**Exponential Functions:** Exponential functions are another form of non-linear functions. Exponential functions are prevalent in economics, representing growth or decay at a constant percentage rate. The population size and compound interest can be modelled using an exponential growth function. It may take the general form of y = a . b^{x}

### 5) Write a note on the importance of functions in economics

Functions play a crucial role in economics in describing and understanding economic relationships, making predictions, and formulating models of economic phenomena. Functions simplfiy complex economic relationships, and are powerful tools for understanding, analysing, and shaping economic outcomes. The importance of functions may be summarised in terms of:

1) **Describing Economic Relationships:** Functions help economists express how variables interact. For example, price and quantity in the demand and supply functions.**2) Cause and Effect:** Functions frequently describe cause and effect relationships. The left-hand side represents the effect while the right-hand side explains the cause/s. For Example, the demand function shows how quantity demanded changes with price.

**3) Predictive Power:** Functions help us make informed predictions. By understanding how variables interact, we can anticipate outcomes. For example, predicting a student’s course grade based on study time, attendance, and prior GPA; or predicting consumer spending based on income and interest rates.

**4) Modelling Economic Phenomena:** Economic models use functions to simplify complex interactions. Functions express relationships like production, utility, and budget constraints.

For example, a production function describes how inputs (like labour and capital) lead to output. The aggregate demand and supply model in macroeconomics is important for the determination of national income, and the explanation of business cycles.

**5) Policy Formulation:** Being a part of economic models functions guide policymakers (e.g., for monetary policy and fiscal policy) in designing effective strategies. For example, guiding the central bank in setting interest rates based on inflation and growth.

### 6) What are the uses of functions in economics ?

Economic theory makes much use of what are called ‘marginal’ concepts Marginal cost, marginal revenue, marginal rate of substitution and marginal propensity to consume are a few example.

Marginal means on the margin or border, and the concept refers to what would happen if there were a small change from the present position.

In economics marginal focuses on understanding how changes in one variable impact another.

Thus, marginal concepts refer to functional relations. If the independent variable X is determining

the dependent variable Y, and we wish to know what would be the change in Y if X changed by a small amount from its present value.

The answer is referred to as the marginal value of Y and is given various names depending on what economic variables X and Y stand for. Marginal analysis guides decision-making by assessing incremental changes in costs, benefits, and revenue.

Note that there are two ways of measuring the marginal value of Y. One is exact and the other is an approximation. Since the exact measure uses differential calculus, introductory texts in economics usually use the approximation which uses only simple algebra.

Besides expressing marginal concepts, the following are some examples of functions commonly used in economic theory:

**In microeconomics:**

a) The production function is a useful way of describing the productive capabilities of a firm. It specifies the maximum output that can be produced with a given quantity of inputs. it is defined for a given state of engineering and technical knowledge. It relates output to inputs.

b) In the microeconomic theory cost and revenue functions, namely marginal cost and marginal revenue, or total cost and total revenue.

c) Demand and supply functions by their interaction determine the price of a good.

d) Elasticity of demand and supply functions. Understanding these elesticities helps economists analyse market dynamics and predict how consumers and producers react to price shifts.

e) Cubic Cost Function. Economists generally use polynomial functions to represent the relationships between costs and output.

f) Breakeven analysis relies on the cost and revenue functions of a firm.

**In macroeconomics:**

a) Consumption function: Used in macroeconomics it shows that the nation’s total disposable income influences the total consumption (spending by household on goods like food, clothing, and housing).

b) The savings function show the relationship between the level of savings and income. The schedule shows amount of savings that the households or a nation will income undertake at each level of income.

c) The investment function explains that investment in the economy is primarily influenced by the state of the business cycle, the cost of investment (determined by interest rates and tax policy), and the state of expectations about the future.

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