 Next topic that is basic tools of economic analysis and optimization technique. Now, what is the learning objectives or session outlines of this topic? We will first look at what are the functional relationship between the economic variables. Then we will discuss some important economic function. Then we will see slope and its use in the economic analysis, derivative of various function, optimization technique and finally, how we do a optimization with a constant. So, coming to the relationship between the economic variable, now what we consider as an economic variable? Any economic quantity, value or rate that varies on its own or due to change in its determinant is an economic variable. Any economic quantity or value or the rate, the variables rate, any variable, when its value whether its rate that changes due to its own or due to change in the determinants of each economic variable. So, when the variable changes the value due to its own value or due to some other factors those are considered as the economic variable. We can take the example that demand for a product whether it is 10 units, whether 12 units and 13 units, every time it is changing a value the demand is not constant. So, this is a economic variable. Price of the product, wage rate, advertising expenditure, these are few examples what we consider as the economic variable where the value get changes either due to own factor or due to change in the determinants of factors affecting the demand for the product. Suppose you take the example why there is a change in the product price or why the price of goods increases, when the cost of production increases. Suppose you take the case of this marker, the cost of production is 10 rupees. So, price is on the basis of 10 rupees when you add a normal profit and attacks with this that becomes the market price for this marker. And suppose the market price of this marker is 13 rupees out of this cost of production is 10. So, what is the determinant of this price of this marker? The cost of production. Now, on what basis there will be increase in the market price of this marker when there will be increase in the cost of production. Suppose the increase in the cost of production has become from 10 rupees to 11 rupees. So, the market price given all other factors the value of all other factors remain constant the market price of this marker will go up by 1 rupees. So, it will go up to it will go till now if it is 13 rupees it was 13 rupees now it is 14 rupees. So, product price in this case the product price is changing due to change in the value of its determinants. So, this is one example of the economic variable. Now, all these economic variables are interrelated and interdependent all the economic variables they are not independent they are interdependent and they are interrelated. This implies that a change in one variable cause a change in the value of other related variables. If they are interrelated and interdependent when value of one variable changes generally that leads to change in the other variable. Suppose we take the example of price and quantity of a product if you take the same example price of marker earlier the price of marker was 13 rupees due to change in the cost of production the price of marker is 15 rupees. Now price and quantity of the product they are interrelated a price is more now if it is from 13 to 15 rupees few customer who cannot effort to pay 15 rupees for that they will not buy this product. So, this increase in price affecting also the quantity of the product what is getting sold in the market. So, price increases that leads to decrease in the some quantity of product that getting sold in the market. So, if you look at price and quantity of product they are interrelated because of that when there is a change in the price or when there is a change in the value of one variable that leads to change in the value of the other variable. In this case typically the price and price of marker gets changed that leads to change in the quantity of the products getting sold in the market. So, if you look at the income and consumption expenditure if your income is more you consume more you spend more if income is less you spend less. So, if you look at income and consumption expenditure they are interrelated. So, value of one get changes due to change in the value of the others. Similarly interest and demand for fund if the interest rate is less more people they go for loan if the interest rate is high there is at least decrease in the demand for loans because the interest rates are on a higher side. So, economic variables are interrelated they are interdependent when there is a change in the value of one variable that leads to change in the value of the other variables because both of them they are interdependent and interrelated. Now, what are the kinds of economic variable? Variable are classified on the basis of economic variable. So, the first category is dependent and independent variable. The value of this variable depends on the value of other variable in case of dependent variable and independent variable the value of this variable changes on their own or due to some exogenous factor. So, dependent variable is one where the value of this variable is always dependent on the value of the other variable and independent value is the value of this variable changes due to their own or may be some exogenous factor, but not due to change in some other variable. So, if you take the example of computer price and demand for computer here demand for computer is dependent computer price is independent because demand for computers is dependent on the computer price when there is a increase in the computer price that leads to decrease in the demand for computers when there is a decrease in the computer price that leads to increase in the demand for computers. So, in a in this typical case the computer price is the independent variable and demand for computer is the dependent variable. Similarly, there is a increase in the petrol price. If you look at now, nowadays there is a increase in the petrol price. Why there is a increase in the petrol price? Because there is a hike in the import oil price. So, in this case, which one is dependent and which one is independent? Petrol price is a dependent variable because petrol price is related with the value of the import oil price. Whenever there is a change in the import oil price, either increase or decrease in the import oil price that leads to change in the value of petrol price. So, if there is a increase in the import oil price that leads to increase in the petrol price, if there is a decrease in the import oil price that leads to decrease in the petrol price. So, in this case, petrol price is dependent, import oil price is independent variable. So, dependent variable is one where the value of that variable is dependent on the other variables and import oil price and sorry the independent variable is 1, where it is not dependent on any other variable for its value, rather the value changes due to own or the exogenous factor. The second kind of economic variable is endogenous and exogenous variable. Now, what is endogenous variable? Endogenous variable is the value of this, the value of this variable is determined within the framework of the analysis model. So, if there is a model between price and quantity, the endogenous variable is 1, where the value of price or value of quantity has to be determined within this specific framework or specific model. And exogenous variable is what? The value of this variable are determined outside the framework of the analysis model. So, any exogenous factor or any external factor will decides what is the value of this exogenous variable. Now, we will take the example of the endogenous and exogenous variable. If you are going to the same petrol price example, domestic oil price is endogenous and international oil price is exogenous variable. So, domestic oil price is dependent on the import oil price. So, in this case the value of the domestic oil price is decided within the framework from the import oil price. However, exogenous variable is internal international oil price, international oil price is not strictly on the basis on the import oil price, it has some other factor and the value of the other factor also decides whatever the international oil price. So, in this case domestic oil price is the endogenous variable whose value is determined within the framework and international oil price is the exogenous variable, which value is decided on the basis of the external factors. Now, when we analyze the relationship between the variables, we can analyze this or we can present the relationship between this variable through three methods. One is tabular method, second one is functional method and third one is graphical method. So, if you are taking the example of price, demand and supply, suppose there are three variables. This relationship between this price, demand and supply, we can present through a graphical analysis, through a supply curve, through a demand curve, taking quantity in the right axis and price in the left axis. We can do a tabular where we can find out what is the demand and supply when the price is 1 rupees, when the price is 2 rupees, when the price is 3 rupees and when the price is 4 rupees. So, this is the tabular representation of the relationship between the variable, this is the graphical relationship between the relationship between this variable and third one is functional which deals with the cause and effect relationship which we analyze or which we present through a functional form. So, in this typical example when we are deciding the relationship between demand and price, it will take a functional form which is equal to Q D which equals to A minus B P where A and B are constant and P is the price of the product and Q is the quantity demanded for this product. So, relationship between three variable can be presented through graphical method, through tabular method or through the functional method. So, tabular and graphical form is useful when number of variables and observations are small. If it is a 2 or 3 variables then tabular and graphical form can be used, but if it is the number of variables are more specifically in case of economic analysis, if you look at all the economic variables are interrelated and interdependent. So, the number of variables and the number of observations are more. So, in this case it always good to use the functional form in order to represent the relationship between this variable. So, most economic problems are complex, it involves a large number of variables because they are interrelated and interdependent and in such cases economist use a mathematical tool known as function to express the relationship between the economic variable. So, the tool is functional and we generally called it a functional representation of relationship between of this relationship between the economic variable and economic analysis it is more useful because there are large number of variables. Next we will see what is a function because function is used to represent the relationship between different economic variables. So, it is a mathematical tool used for expressing the relationship between economic variable that have a cause and effect relationship. When they are interrelated if one is cause and other is effect and it is a relationship between different economic variable it is a mathematical tool. Function is a mathematical tool used for expressing the relationship between the economic variables. There are two types of functions. One is bivariable function and second one is the multivariable function. Bivariable function involves only two variables and multivariable function one dependent and more than one independent variable. In case of bivariable function it has only two variables one is dependent and other is independent. In case of multivariable function, there is only one dependent and more than one independent variables. Now, we will take an example to understand this bivariate function and multivariate function. If the value of variable x depends on value of variable y, then the relationship between two each y is a function of x, where y is the dependent variable and x is the independent variable. This is a typical function which express the relationship between y and x, where y is the dependent variable and x is the independent variable and y is a function of x. Now, taking the example of a demand function, if you consider p is the price of the product and d p is the demand for the product, the demand for the product is always dependent on the price for the product. So, in case of a bivariate demand function, when we are taking that there is only one dependent variable and one independent variable, in this case we use this function d p is a function of p and this is a bivariate demand function, where the demand for the product is dependent only on price. Now, suppose we assume that demand for the product is not only dependent on the price, it is also dependent on the income which is represented through y, dependent on a that is advertising expenditure and also dependent on the taste and preference of the consumer. So, in this case how we represent the relationship between the variable price, demand for the product, income, advertising expenditure, taste and preference of the consumer through a function. We know that demand for a product is dependent on price for the product, income for the product, advertising for the product and taste and preference for the product. So, demand for the product is a function of price, income, advertising expenditure and taste and preference. So, this is the example of a multivariate demand function, where there are four independent variable and one dependent variable. Here the dependent variable is d p and it is dependent on four independent variable that is p, y that is p is price of the product, y is the income of the product, a is the advertising expenditure associated to the product and t is the taste and preference for the consumer of the consumer for the product. So, there are two types of functions one is bivariate and other is multivariate. Bivariate essentially deals with two variables and multivariate deals with one dependent variables and number of independent variables. Now, how do we specify a function on the basis of the nature of the relationship, how both of them are related, whether they are positively related, whether they are negatively related and second is on the basis of the quantitative measure of the relationship or the degree of relationship. If they are positive they are negative up to what extent, what is the, how we can quantify the degree of relationship that is on that basis we can specify a function. Generally, we use a regression technique for specification and quantification. Now, look at this example, suppose we take a demand function which is 500 minus 5 p. What are the different implication of this demand function or how we can analyze this demand function, when the price is 0 demand is equal to 500 units because the intercept value is 500. So, the first implication is at 0 price demand is equal to 500 units. There is a negative 5 p, so negative source there is a inverse relationship between the price and demand. This is the nature of relationship between price and demand is inverse and the value 5 implies that for each 1 rupees change in the price demand change by 5 units. So, 1 rupees change in the price leads to 5 unit change in the demand. So, this is the degree of relationship between the price and quantity demanded. So, at 0 price demand is equal to 500 units. So, when you get the product at free the price the demand is 500 units. What is the significance of this minus that shows the nature of relationship between 2 variables and the nature of relationship is inverse. There is a inverse relationship between the price and the demand and 5 implies that for each 1 rupees change in the price demand change by 5 units. So, if you look at there is a 5 time change in the if you have quantity demanded when there is a 1 time change in the price. This is the quantification of the relationship or the degree of the relationship. Now, what is the general form of a demand function? The general form of a demand function is q x is equal to a minus p p x, where q x is the quantity of x, p is the price of x and a and b are the constant. So, constant in a function are called the parameters of the function and what is the role of this parameters? The parameters of the function specify the extent of relationship between the demand and between the dependent and independent variable. So, this a and b they will specify what is the extent of relationship between the dependent and independent variable. They will talk about the nature of the relationship and the degree of relationship between dependent and independent variable. So, in taking this demand function q x is equal to a minus b p x, here constant a gives the limit of q x when p x is equal to 0. And b is the coefficient of variable p x which measures the change in the q x as a result of change in the p x. So, this is basically the change in the q x which is equal to minus b and the change in the p x. So, in the previous example if you remember d was equal to 500 minus 5 p. So, 500 was the value of a which gives the limit of q x when p x is equal to 0. So, when price was equal to 0, 500 was the quantity demanded and b is the coefficient of the variable p x. So, in the if you look at in the previous example 5 p. So, 5 p is the value of b which is the coefficient of variable p x which measures the change in the q x as a result of change in the p x which was 5 times because the change in the q x was 5 which we can get through the value of b and change in the p x is 1. So, when in the previous example when there is a one time change in the price that leads to 5 times change in the quantity demanded. So, there are few other function like demand function and other thing like production function cost function that we will discuss in the next session. And for this specific part like basic optimization technique and basic economic analysis we have followed this managerial economics d and d by d of 7th edition. Thank you.