 a formal model of consumption and saving, the budget constraint. So, to keep our model simple we are taking some assumptions. First assumption is that, our analysis is for two time periods, ok. A present period and another future period. We are taking it so that we can graphically do it in a two dimensional space. So, that is why we are taking our time period 2. And with this we are taking some more values, current income. We are assuming that this is given. We are also using numerical values so that we can understand later things. So, current income Y is 42,000. Future income B, we are assuming that we know today. And there is no uncertainty in this. This is 33,000. And in the start of the present period we are denoting the wealth available from A and this is also given. Its value is 18,000. And interest rate is 10%. So, we are taking some values. We will construct our budget constraint. So, choice variable. These were the variables that we had given. Current income, future income, current value of wealth and the interest rate. The choice variable that we have chosen, which the consumer has to maximize their utility, we have chosen the choice variable. Another A F, A F stands for wealth at the beginning of the future period. Second C, current consumption. This is its choice variable. How much it wants to consume today and how much it wants to consume in the future period. So, these are its three choice variables. Current consumption, future consumption and wealth at the beginning of the future period. Okay. A F, wealth at the beginning of the future period. If we define this. So, this is Y, what is Y? Y is your current income plus A, A is your current amount of wealth. Okay. These are total available resources in the current period. Y plus A. Minus C, C is your current consumption. So, when you minus C from Y plus A, this will be your saving. Actually, we define saving as Y minus C. So, these were total available resources. Y plus A and C, we have spent them. So, the rest are available for the future period. And these available resources are in the future period. When we invest them, we will get some interest on it. So, how much will be the total? You know to calculate it. We will multiply it by one plus R. We will use numerical value. For Y, we assume 42,000. For A, we assume 18,000 minus C into 1 plus 0.1. 0.1 means 10% interest rate. So, in this formula, if we know the value of C, then we can determine the value of future wealth for any value of C. And from this, we will get future consumption. Cf is the future consumption. Okay. And Y plus A minus C into 1 plus R, what was this? You had wealth available in the future period. And Yf is the income, which you will earn in the second period. So, the first period is carrying some resources for the second period. And plus, in the second period, it is earning some resources. So, all of these will be available in the second period. And since we have assumed that its lifespan is just in two periods, so, all the resources available in the second period will be spent in the second period. So, Cf will be equal to this. So, in this context, we will call the budget constraint. We will put numerical values. So, these values are above, okay. And plus 33,000 is its future income. We will add it. So, these total available resources will be for consumption in the second period. So, obviously, it cannot spend more than these resources. That is why this is its budget constraint. And graphically, if we want to understand all this, then I told you that we have two-time periods. So, in two-dimensional space, we can understand this. On horizontal axis, we are taking current consumption and on vertical axis, we are taking future consumption. So, on horizontal axis, this intercept value of 90,000, if we use the numerical values, then what was it? In the last slide, I will show you that it had current income of 42,000, right? And it had initial wealth of 18,000 and it had 33,000 in the future. So, 33,000 was converted to its present value. So, the total 90,000 is available to it. This means that if it zeroes its future consumption, then in the current period, at the most, consumer can consume 90,000. And the intercept of the vertical is 99,000. We will calculate all these values again. So, what is this? When its current consumption is zero, then at the most, it can consume 99,000 in the second period. And this is the budget constraint. This budget constraint actually reflects all the combinations of current consumption and future consumption, the combination on which they are finding out their total lifetime resources. Okay? For example, if you want to understand point B, then what is B? B is showing that in the current period, its consumption is 15,000 and in the future period, its consumption is 82,500. Okay? You can understand this in this way that if it zeroes its current consumption, then at the most, it can consume 99,000 in the future. But since it is consuming 15,000 in the current period from that 99,000, then due to this, its future consumption becomes so low. And so on. Similarly, we will discuss all the C, D, E and other points. These are the combinations that are the values of C and CF on which its total lifetime resources are exhausted. It is a negatively sloped line. Why? Because whenever you increase the current consumption, then you will have to reduce the future consumption. That's why it is negatively sloped. And what will be its slope? It will be determined by interest rates. Okay? Interest rate will be as steep as this line and the less the interest rate, the less the line will be. We assume this as 10%. That's why it is 1.10. We will discuss all this in another context as well. Present value and future value. You must be familiar with this concept of finance in some course. The simple concept is that if a person has 100 feet today, and if he keeps it in the bank and has a 10% interest rate, then he will get it at 110 after a year. So, the present value of the amount that is going to be 110 after a year is 100 rupees. Or the future value of today's 100 rupees is 110. Okay? How do we calculate this? It is a simple formula. Present value is equal to future value divided by 1 plus i. If you are talking in nominal terms, then i is the nominal interest rate. And if you are talking in real terms, then you will use real interest rate instead of i. So, present value and future value, that is, if you want to convert the future to your present, then you will divide it by 1 plus i. If you want to convert the present to your future, then you will multiply it by 1 plus i. Present value of lifetime resources. PVLR. That is, the lifetime of the individual is equal to the current period and future period. Right? What was available to him in the current period? One is income. Why? What he was working on is the labor services. Okay? Plus, the wealth he had, A, is available in the present period. And YF had to be available in the future in the second period. And to convert it to YF in the present value, I just told you that we are dividing it by 1 plus r. So, in this way, you have total lifetime resources which become its present value. And in this way, if you want to understand the present value of lifetime consumption, then C is the consumption of its present value. Okay? And CF's future was in the period of consumption. And when you want to convert the future period of consumption to the present value, then the formula is the same. We will divide it by 1 plus r. So, this will be the present value of future consumption. So, you have this equation C plus CF over 1 plus r. This is the present value of lifetime consumption. And what is the budget constraint? Budget constraint, this is simple. That its present value of lifetime consumption should be equal to the present value of lifetime available resources. So, if you equate these two, then it will become its budget constraint. So, I will show you once again from the budget line. That 90,000 is the present value of the lifetime resources. And 99,000 is the future value of the lifetime resources. So, the different points that come on this budget line in both the present consumption and the future consumption show different combinations. This triangle, this triangle shows that it has space available. The consumer cannot go out of this space. He can choose the current and future consumption pair which is present on the boundaries of this triangle. Any point outside of this triangle is unattainable for him. So, this was the concept of the budget constraint.