1 00:00:17,570 --> 00:00:25,840 Good morning. Welcome to the sixth lecture on Economics, Management, and Entrepreneurship. 2 00:00:25,840 --> 00:00:37,500 In the last 5 lectures, we had covered basics of microeconomics theory. Today, we shall 3 00:00:37,500 --> 00:00:48,510 discuss certain exercises on those theories that we had developed in the last 5 classes 4 00:00:48,510 --> 00:00:58,840 and it will hopefully give you much more insights into the real life applications of the basic 5 00:00:58,840 --> 00:01:10,869 microeconomic theory that we have discussed in the last 5 lectures. I have covered 2 or 6 00:01:10,869 --> 00:01:21,570 3 exercises from relevant to each of the lectures as you will see. 7 00:01:21,570 --> 00:01:31,030 The first exercise that I take is from the demand supply and market equilibrium lecture. 8 00:01:31,030 --> 00:01:43,790 This is a problem on demand function for TV sets is given as Q equal to minus 2000 P plus 9 00:01:43,790 --> 00:01:56,780 1000 Y plus 0.01 POP, where P is the prize of a TV set, Y is the disposable income of 10 00:01:56,780 --> 00:02:09,520 a person in a year, and POP is population. This expression is developed on the basis 11 00:02:09,520 --> 00:02:24,590 of data and it is assumed that this equation defines the demand function for TV sets. Three 12 00:02:24,590 --> 00:02:26,110 questions are asked. 13 00:02:26,110 --> 00:02:35,190 Find the demand function and plot the demand curve for TV in a year, if the disposable 14 00:02:35,190 --> 00:02:49,359 income Y is 16,000 per year per person, and POP is 900 million persons. That means Y and 15 00:02:49,359 --> 00:03:00,500 POP values are given and we are required to find out relationship containing Q with P. 16 00:03:00,500 --> 00:03:07,829 The second part of the question is if the price of a TV set is 10,000 rupees per set 17 00:03:07,829 --> 00:03:16,769 find the quantity demanded. The third part is population remaining same the disposable 18 00:03:16,769 --> 00:03:26,190 income is 11,000 rupees per year per person instead of 16,000 which was given here. 19 00:03:26,190 --> 00:03:33,540 Suppose that it comes down to 11,000 then plot the demand curve. So first thing is that 20 00:03:33,540 --> 00:03:40,630 we are starting with this particular equation something like regression equation where a 21 00:03:40,630 --> 00:03:48,660 demand function for Q is a given as a function of P, Y, and POP and we are required to find 22 00:03:48,660 --> 00:03:57,780 out relationship containing Q with P for Q with P given the values of Y and POP. 23 00:03:57,780 --> 00:04:03,630 It is straight forward what we do to solve the first part of the problem. Firstly, these 24 00:04:03,630 --> 00:04:13,040 are given this equation is given and these are the initial values given. The first question 25 00:04:13,040 --> 00:04:23,570 is find the relationship between Q and P. So if I put values of Y here and of POP here, 26 00:04:23,570 --> 00:04:38,880 then I get a constant which is 25 million. So Q is equal to minus 2000 P plus 25 million 27 00:04:38,880 --> 00:04:55,910 and P thus equal to 12,500 minus 0.0005 Q. So if I plot P against Q it will have a negative 28 00:04:55,910 --> 00:05:07,400 slope equal to minus 0.0005 that is what I have shown here minus 0.0005 the intercept 29 00:05:07,400 --> 00:05:20,270 is 12,500 so this is 12,500 and the slope is minus 0.0005. 30 00:05:20,270 --> 00:05:32,230 The second part of the question is (() that if P equal to 10,000 then what is the 31 00:05:32,230 --> 00:05:42,430 value of Q. P we know the relationship between Q and P Q equal to this so the value of P 32 00:05:42,430 --> 00:05:51,700 is given as equal to 10,000. The estimated value of Q is 10,000 into minus 2000 that 33 00:05:51,700 --> 00:06:01,990 is minus 20,000 when we subtract that from 25,000 this becomes 20 million and we subtract 34 00:06:01,990 --> 00:06:07,840 that from 25 which gives us 5 million deficits so that is the second part of the question. 35 00:06:07,840 --> 00:06:18,350 The third part of the question is if instead of Y which is given as 16,000 rupees per year 36 00:06:18,350 --> 00:06:27,480 per person suppose that the disposable income reduces from 16,000 to 11,000, population 37 00:06:27,480 --> 00:06:38,060 remaining same then, what is the demand function and what is the demand plot the demand curve. 38 00:06:38,060 --> 00:06:46,330 So what we need to do is just put the value of y as equal to 11,000 and not 16,000 and 39 00:06:46,330 --> 00:06:56,960 put POP equal to 900 million as it was so that gives us a value Q equal to the coefficient 40 00:06:56,960 --> 00:07:00,040 of P does not change, only the constant changes. 41 00:07:00,040 --> 00:07:07,960 It was earlier 25 million now it has become 20 million. So intercept, so P equal to 10.000 42 00:07:07,960 --> 00:07:22,980 minus this. So, the coefficient of Q is minus 0.00005. Here also it remains the same. Only 43 00:07:22,980 --> 00:07:34,310 the intercepts change from 12,500 it has come down to 10,000 which means that for this reduced 44 00:07:34,310 --> 00:07:42,690 disposable income the demand curve is a straight line which is parallel to the original line. 45 00:07:42,690 --> 00:07:50,510 This is the original line for Y equal to 16,000, POP equal to 900 million persons. So, this 46 00:07:50,510 --> 00:08:02,050 is shifted to the left, the slope of this line remaining the same as, 0.00005 negative. 47 00:08:02,050 --> 00:08:05,260 This is the first question. 48 00:08:05,260 --> 00:08:14,639 Now we come to exercise 2. Now, this is an example, where an earlier study has indicated 49 00:08:14,639 --> 00:08:26,639 that the supply function for TV sets is given as a function of price of the TV set, price 50 00:08:26,639 --> 00:08:35,550 of a competing product such as a music set then the labour cost that is price of labour 51 00:08:35,550 --> 00:08:46,161 and the input duty or Tariff on imported TV set. So these are defined here PC, PL, and 52 00:08:46,161 --> 00:08:58,371 Tariff and this is the estimated regression equation that relates Q with P, PC, PL, and 53 00:08:58,371 --> 00:08:59,710 T. 54 00:08:59,710 --> 00:09:08,260 Three parts of the question are given here. The first part is find the supply function 55 00:09:08,260 --> 00:09:20,520 and plot the supply curve for TV in a year when values of PC, PL, and T are given. If 56 00:09:20,520 --> 00:09:26,940 the price of TV set is 10,000 rupees, find the quantity supply other values remaining 57 00:09:26,940 --> 00:09:36,750 same. If the value of T changes from the earlier value of 2000 rupees to a new value 1,000 58 00:09:36,750 --> 00:09:44,380 rupees then how will this supply function change? Now let us take out this particular 59 00:09:44,380 --> 00:09:47,760 exercise. 60 00:09:47,760 --> 00:10:01,680 So given the regression equation containing Q. P, PC, PL, T values of PC, PL, and T are 61 00:10:01,680 --> 00:10:12,040 given and when I put these values here for PC 8,000, for PL 80,000 for T 2,000 I get 62 00:10:12,040 --> 00:10:24,240 the relationship containing Q between Q and P such as this from here I can find P which 63 00:10:24,240 --> 00:10:35,800 is 7500 plus 0.0005 Q. So the intercept is 7,500 and the slope of this line is 0.0005. 64 00:10:35,800 --> 00:10:46,000 So I plot this one here. This curve is the supply curve having a positive slope whose 65 00:10:46,000 --> 00:10:59,490 value equal to 0.0005 and if P equal to 10,000 if P equal to 10,000 the value of Q is given 66 00:10:59,490 --> 00:11:11,140 as 10,000 into 2,000 that makes it 20 million minus 15 million so that gives 5 million sets. 67 00:11:11,140 --> 00:11:17,940 Now the third part of the question is if other values remain same, but only T changes from 68 00:11:17,940 --> 00:11:26,300 the given value of 2000 to 1000, then how will the relationship between Q and P changes. 69 00:11:26,300 --> 00:11:36,690 The demand curve will have an equation. You put the values here. T equal to 1000 so Q 70 00:11:36,690 --> 00:11:50,260 becomes 2000 P minus 13, 500,000 and from here I can find P. The intercept is 6,750 71 00:11:50,260 --> 00:12:01,060 corresponding to the point here 6,750 and the slope is exactly same positive and the 72 00:12:01,060 --> 00:12:09,029 value both are same so this line is parallel, but the intercept being lower than the previous 73 00:12:09,029 --> 00:12:20,930 value it means that as T is reduced it shifts to the right. So this is the exercise 2. 74 00:12:20,930 --> 00:12:28,870 Now we go to exercise 3. Here, we are trying to find out the equilibrium value and there 75 00:12:28,870 --> 00:12:38,390 are 2 ways one is floating graphically. This is our demand curve with a negative slope. 76 00:12:38,390 --> 00:12:45,649 This is our supply curve that has a positive slope. The point of intersection gives the 77 00:12:45,649 --> 00:12:55,800 equilibrium value of price and output. In this case, the value is obtained as 10,000 78 00:12:55,800 --> 00:13:05,339 rupees per set and this is 5 million TV sets in a year. Analytically also one can find 79 00:13:05,339 --> 00:13:06,930 this value. 80 00:13:06,930 --> 00:13:14,970 Plot find the demand function that we have already generated which is minus 2000 P plus 81 00:13:14,970 --> 00:13:24,029 25 million and supply function we have already found out Q equal to 2000 P minus 15 million 82 00:13:24,029 --> 00:13:30,980 so equate them at the equilibrium point at the equilibrium and we will get this equal 83 00:13:30,980 --> 00:13:40,700 to this and that will give us a value of Q and P the equilibrium values of 10,000 for 84 00:13:40,700 --> 00:13:53,839 price and 5 million TV sets as the output of the quantity. This is exercise 3. 85 00:13:53,839 --> 00:14:05,920 Now we come to exercise 4 in this example this exercise we are given price and output 86 00:14:05,920 --> 00:14:13,860 for a particular product in these 2 columns quantity and price and we are required to 87 00:14:13,860 --> 00:14:25,500 find out the total revenue, marginal revenue, and average revenue. Now total revenue is 88 00:14:25,500 --> 00:14:27,760 nothing but 89 00:14:27,760 --> 00:14:38,310 Q into P is also known as sales or total sales or sales revenue or total revenue. It is just 90 00:14:38,310 --> 00:14:45,250 the total amount obtained by selling this amount of this quantity of goods. So nothing 91 00:14:45,250 --> 00:14:53,680 is sold, so the revenue is 0, total revenue is 0. One at a price of 75 therefore the revenue 92 00:14:53,680 --> 00:15:10,640 is 75 into 1 75. Suppose the price is 70, quantity is 2, so it is 140. If 3, it is 65 93 00:15:10,640 --> 00:15:17,480 these are given so just multiply. So product of Q and P is basically equal to TR and is 94 00:15:17,480 --> 00:15:18,720 found out. 95 00:15:18,720 --> 00:15:30,470 This column gives the total revenue for this quantity sold. Now marginal revenue is if 96 00:15:30,470 --> 00:15:41,930 quantity increases by 1 then what is the increment of revenue. So from 0 to 1 the increment is 97 00:15:41,930 --> 00:15:54,610 75. 75 minus 0 is 75. From 1 to 2 total revenue increases from 75 rupees to 140 rupees so 98 00:15:54,610 --> 00:16:03,970 the increment in total revenue is 140 minus 75 which is equal to 65. Similarly from quantity 99 00:16:03,970 --> 00:16:12,420 2 to 3, the total revenue increases from 140 to 195 giving an increment of 55 that is the 100 00:16:12,420 --> 00:16:15,029 marginal revenue. 101 00:16:15,029 --> 00:16:21,290 So the marginal revenue is calculated in this manner and you will see that marginal revenue 102 00:16:21,290 --> 00:16:41,380 reduces and becomes negative and even more negative as quantity increases and price reduces. 103 00:16:41,380 --> 00:16:52,970 Now average revenue is nothing but total revenue by quantity and in this case, it is same as 104 00:16:52,970 --> 00:17:07,709 price. Of course, 75 by 1 is 75. This AR cannot be found out. Sorry this should not have a 105 00:17:07,709 --> 00:17:19,519 0 there. It should be a hyphen here, because 0 by 0 is nothing. 75 by 1 is 75. 140 by 2 106 00:17:19,519 --> 00:17:36,879 is 70, 195 by 3 is 65, 240 by 4 is 60, 275 by 5 is 55, so basically this quantity, this 107 00:17:36,879 --> 00:17:48,230 average revenue is same as price excepting for the first one. So this is how we find 108 00:17:48,230 --> 00:17:54,299 out total revenue, marginal revenue and average revenue. 109 00:17:54,299 --> 00:18:07,259 Now, we come to our next exercise and this says, assume that a company with the name 110 00:18:07,259 --> 00:18:14,460 ABC electronics has the following total revenue and total cost functions. So total revenue 111 00:18:14,460 --> 00:18:26,869 function is given in this fashion and total cost is given in this fashion and where Q 112 00:18:26,869 --> 00:18:35,239 is the quantity produced. Find the profit function and hence find the optimum output 113 00:18:35,239 --> 00:18:38,279 that maximizes the profit. 114 00:18:38,279 --> 00:18:46,480 Now that we know total revenue and total cost we can find a profit function and we can optimize 115 00:18:46,480 --> 00:18:53,399 the profit. We can find out the value of Q that maximizes the profit that is what is 116 00:18:53,399 --> 00:18:58,960 the first part of the question? The second part of the question is show that the profit 117 00:18:58,960 --> 00:19:07,210 is maximum when the marginal revenue equal to marginal cost. So this is exercise 5. We 118 00:19:07,210 --> 00:19:11,470 go to the solution in this fashion. 119 00:19:11,470 --> 00:19:18,570 Define first of all that the profit function pi is given by the difference between the 120 00:19:18,570 --> 00:19:25,779 total revenue and the total cost. So total revenue minus total cost is the total profit 121 00:19:25,779 --> 00:19:34,879 made and then we find out profit function and then we differentiate the profit function 122 00:19:34,879 --> 00:19:44,669 with respect to Q to find out the optimum value of Q that maximizes profit. So what 123 00:19:44,669 --> 00:19:53,749 we do here. This is pi, the profit function is total revenue minus total cost so you subtract. 124 00:19:53,749 --> 00:20:04,309 When we subtract the 2 we get this that is minus 1500 plus 110 Q minus Q square. So this 125 00:20:04,309 --> 00:20:15,039 is a function of Q. So take the first derivative d pi by dQ we get 110 minus 2 Q put that equal 126 00:20:15,039 --> 00:20:24,340 to 0. So this is the necessary condition for a function to be maximum or minimum. The first 127 00:20:24,340 --> 00:20:33,499 derivative must be equal to 0 and that gives the value of Q equal to 55. To find out whether 128 00:20:33,499 --> 00:20:41,200 this value of Q minimizes or maximizes pi, we go to the second derivative. 129 00:20:41,200 --> 00:20:52,090 Second derivative is minus 2 which is less than 0 it means that at this value of Q pi 130 00:20:52,090 --> 00:20:59,609 must be maximum. So the first part of the question which is find the profit function 131 00:20:59,609 --> 00:21:07,809 it is subtracting TC from TR which is this and the optimum value of Q that maximizes 132 00:21:07,809 --> 00:21:16,210 profit is 55. We have tested that it gives the maximum value. The second part of the 133 00:21:16,210 --> 00:21:22,800 question was that show that at that optimum point MR equal to MC. 134 00:21:22,800 --> 00:21:31,139 It is very straight forward. Pi equal to profit equal to total revenue minus total cost which 135 00:21:31,139 --> 00:21:36,990 is written here. If I take the first derivative with respect to Q which we have done here 136 00:21:36,990 --> 00:21:45,549 that is nothing but first derivative of TR minus first derivative of TC. The first derivative 137 00:21:45,549 --> 00:21:53,289 of TR with respect to Q is nothing but MR and the first derivative of TC with respect 138 00:21:53,289 --> 00:22:03,059 to Q is nothing but marginal cost and since d pi by dQ has to be equal to 0 when it is 139 00:22:03,059 --> 00:22:10,159 maximum MR must to be equal to MC. So it is very straight forward this is the second part 140 00:22:10,159 --> 00:22:13,080 of this exercise. 141 00:22:13,080 --> 00:22:24,520 To exercise 6, this exercise deals with arc elasticity. Now, if you read this exercise 142 00:22:24,520 --> 00:22:34,170 during February, in an effort to reduce the end-of-the-year inventory, an auto break assembly 143 00:22:34,170 --> 00:22:43,940 manufacturer offered rupees 6,000 discount from the existing rupees 60,000 sticker price, 144 00:22:43,940 --> 00:22:58,770 on each break assembly. The monthly sale rose from 15 to 23 on account of this price discount. 145 00:22:58,770 --> 00:23:07,510 Now you see that the change is something like 10% which is higher than 5%. 146 00:23:07,510 --> 00:23:17,090 And if you recall whenever there is a price change of more than 5% we go for computing 147 00:23:17,090 --> 00:23:21,740 the arc elasticity of demand. The question therefore is given. So the question therefore 148 00:23:21,740 --> 00:23:31,970 is given is to calculate the arc elasticity for this break assembly and the second part 149 00:23:31,970 --> 00:23:39,019 is quite interesting it says calculate the sticker price reduction necessary to eliminate 150 00:23:39,019 --> 00:23:47,820 the manufacturer's remaining inventory of 27 assemblies during the next month. 151 00:23:47,820 --> 00:23:58,599 Come to the solution part. This is the diagram that shows the situation. Now, this is the 152 00:23:58,599 --> 00:24:07,869 demand function for the autobreak assembly. Now, the operating point is here that initially 153 00:24:07,869 --> 00:24:17,859 the price was 60,000 and the quantity demanded in the market were just 15 and the manufacturer 154 00:24:17,859 --> 00:24:25,080 reduced the price by giving a discount of 6,000 rupees bringing down the price from 155 00:24:25,080 --> 00:24:34,149 60,000 to 54,000 and that resulted in an increase in the value of Q2. 156 00:24:34,149 --> 00:24:44,029 Now this reduction is as you can see is 10% quite high therefore arc elasticity calculation 157 00:24:44,029 --> 00:24:51,799 is relevant here rather than point elasticity calculation and according to our equation 158 00:24:51,799 --> 00:25:04,919 for arc elasticity it is the change in the quantity by the average quantity by change 159 00:25:04,919 --> 00:25:16,820 in the price by the average price which results in this expression Q2 minus Q1 by P2 minus 160 00:25:16,820 --> 00:25:27,210 P1 and P2 plus P1 by Q2 plus Q1. This division by 2 cancels out. 161 00:25:27,210 --> 00:25:38,139 So we have price elasticity of demand that is arc elasticity is given by this expression. 162 00:25:38,139 --> 00:25:54,090 Now put the values of Q2, Q1, P2, P1, etc and we get a value of arc elasticity as equal 163 00:25:54,090 --> 00:26:06,109 to minus 4. Now the second part of the question is at the end of the month there are 27 break 164 00:26:06,109 --> 00:26:16,230 assemblies available if the arc elasticity is minus 4 then what should be the price at 165 00:26:16,230 --> 00:26:27,980 which it can be sold so that all the 27 can be sold out that means if this Q3 is 27 what 166 00:26:27,980 --> 00:26:40,130 is the value of P3. So we use the same relationship except in that instead of P2 we now write. 167 00:26:40,130 --> 00:26:48,720 We do not take the old value of P2, this actually is P3. So instead of P2 it should be P3, P3 168 00:26:48,720 --> 00:26:54,799 and P3 and P3, therefore this changes should be done. So I am just putting these values 169 00:26:54,799 --> 00:27:08,479 here so this expression gives a value of P3 equal to 52,000, P3 minus P1 equal to minus 170 00:27:08,479 --> 00:27:18,470 8000 that means a further discount of 8000 rupees per break assembly should be given 171 00:27:18,470 --> 00:27:29,509 and that will enable the manufacturer to sale out its remaining 27 inventory break assemblies. 172 00:27:29,509 --> 00:27:33,789 So this is example 6 or exercise 6. 173 00:27:33,789 --> 00:27:45,580 Now we go to exercise 7. Exercise 7 is likewise quite interesting. It says that video station 174 00:27:45,580 --> 00:27:56,460 sells video recordings of movies and also sells blank cassettes for home recording. 175 00:27:56,460 --> 00:28:05,929 Now during Puja holidays, video station reduced its prices as follows: For video recording 176 00:28:05,929 --> 00:28:17,469 it reduced its price from rupees 29.99 to rupees 24.97 and for blank cassettes it reduced 177 00:28:17,469 --> 00:28:24,059 its price from rupees 19.99 to rupees 14.97. 178 00:28:24,059 --> 00:28:34,309 The trade association in a recent study has estimated the point price elasticity to be 179 00:28:34,309 --> 00:28:43,210 as follows: For video recording it has found out a value of minus 1.5 and for blank cassettes 180 00:28:43,210 --> 00:28:54,559 it found out a value of minus 4. Now in the right of this trade associationâ€™s recommendations 181 00:28:54,559 --> 00:29:02,909 are estimated values of the point elasticities. are the new prices justified meaning these 182 00:29:02,909 --> 00:29:14,590 prices that the video station is now charging is it justified if the unit cost of manufacturing 183 00:29:14,590 --> 00:29:21,450 that is unit cost of preparing a video recording and having a blank cassette are rupees 10 184 00:29:21,450 --> 00:29:30,029 and rupees 8 respectively. This is the question. Is it justified? 185 00:29:30,029 --> 00:29:44,399 Now recall the relationship between the marginal revenue, price, and 186 00:29:44,399 --> 00:29:56,519 point price elasticity epsilon P. Marginal revenue equal to d by dQ of TR that is unit 187 00:29:56,519 --> 00:30:04,799 change in Q brings in how much change in the total revenue. Total revenue is nothing but 188 00:30:04,799 --> 00:30:14,519 price into quantity PQ and as we know P is a function of Q so if you take the derivative 189 00:30:14,519 --> 00:30:24,659 it is first function as it is into the derivative of the second so, P into derivative of the 190 00:30:24,659 --> 00:30:33,029 second means, d by dQ which is 1 plus derivative of the first function, which is dP by dQ into 191 00:30:33,029 --> 00:30:53,139 Q. So MR equal to this which is equal to P1 plus dP by dQ keep it like this. 192 00:30:53,139 --> 00:31:04,950 And here it is Q by P is take P here and Q here, so it becomes dP by P, dQ by Q and this 193 00:31:04,950 --> 00:31:16,419 is nothing but P taken outside 1 plus 1 by dQ by Q by dP by P and this by definition 194 00:31:16,419 --> 00:31:24,879 is the point price elasticity of demand that means a small change in P, a fractional change 195 00:31:24,879 --> 00:31:31,659 in P gives rise to how much fractional change in Q that is epsilon P. So, the relationship 196 00:31:31,659 --> 00:31:40,730 between marginal revenue, price and elasticity are these things. Now, at the equilibrium 197 00:31:40,730 --> 00:31:49,330 as we already have seen marginal revenue equal to marginal cost. 198 00:31:49,330 --> 00:31:57,349 Hence the equilibrium prices at which this relationship will hold are the following: 199 00:31:57,349 --> 00:32:03,179 As you know marginal cost for video recording is given as rupees 10 that will be equal to 200 00:32:03,179 --> 00:32:16,159 price of video recording into 1 plus 1 by epsilon P, so 1 plus 1 by minus 1.5, the value 201 00:32:16,159 --> 00:32:25,039 that the trade association has estimated. Now if I solve this equation I get the value 202 00:32:25,039 --> 00:32:37,049 of price of video recording which is 30 rupees whereas the new prices that the company is 203 00:32:37,049 --> 00:32:46,720 charging is only 24.97 that means this reduction is not justified. 204 00:32:46,720 --> 00:32:56,320 Now we go for the blank cassettes. Blank cassettes the marginal cost for the company for blank 205 00:32:56,320 --> 00:33:05,219 cassette is rupees 8. Using the same relationship with the new value of epsilon P as estimated 206 00:33:05,219 --> 00:33:11,489 by the trade association, which is equal to minus 4. The value of the blank cassettes 207 00:33:11,489 --> 00:33:26,480 would be the price should be set up 10.67 therefore setting rupees 8 is the setting 208 00:33:26,480 --> 00:33:37,570 the price as rupees 14.97 is also not justified it should be reduced to 10.67 whereas for 209 00:33:37,570 --> 00:33:46,029 video recording it should be increased to rupees 30. So the new prices that the company 210 00:33:46,029 --> 00:33:53,710 is charging are not justified. Now you can see from this example that elasticity knowing 211 00:33:53,710 --> 00:34:02,679 the value of elasticity helps in fixing the prices. Now we got to the next example. 212 00:34:02,679 --> 00:34:14,669 The next example, next exercise, this exercise is on demand estimation and demand forecasting. 213 00:34:14,669 --> 00:34:23,339 We start with a very simple example where we show that the annual sales exercise is 214 00:34:23,339 --> 00:34:33,930 like this. Annual sales of Babu restaurant are as follows in thousand rupees: Starting 215 00:34:33,930 --> 00:34:46,551 from annual sales so some year, let us say 2000, this is 2001, 2002 like that up to 2011 216 00:34:46,551 --> 00:34:55,850 and 284 thousand rupees, 266 etc follows like this and we are required to find out the annual 217 00:34:55,850 --> 00:35:07,860 rate of growth assuming a constant growth rate with annual compounding. Make a 5-year 218 00:35:07,860 --> 00:35:09,770 forecast. 219 00:35:09,770 --> 00:35:23,150 So basically we are assuming that here that the growth of sale quantity sold at time t 220 00:35:23,150 --> 00:35:35,930 follows a power function, follows a growth such as this Q0 into 1 plus g to the power 221 00:35:35,930 --> 00:35:47,970 t. Q0 is the sale in the year 2000 and g is the annual growth rate and to the power t. 222 00:35:47,970 --> 00:35:58,910 So this is the annual growth rate that means in the starting from 2000, 2001 sale is expected 223 00:35:58,910 --> 00:36:09,810 to be 2000 sale into 1 plus g. 2002 sale will be 2000 sale into 1 plus g to the power 2 224 00:36:09,810 --> 00:36:20,100 so on and so forth. So from here suppose that we put the 2011 value as 568 and 2000 figure 225 00:36:20,100 --> 00:36:29,650 as 284 and t is 10. 226 00:36:29,650 --> 00:36:41,100 Then this is the relationship from here we get 2 equal to 1 plus g to the power 10, therefore 227 00:36:41,100 --> 00:36:57,650 ln 2 equal to 10 ln 1 plus g. There is a mistake here there should be 10 ln 1 plus g and that 228 00:36:57,650 --> 00:37:09,160 gives a value g equal to 0.0718. So, this is the annual growth rate that is 7.18% and 229 00:37:09,160 --> 00:37:18,240 suppose that we are asked to find out or estimate 5-year hence sale forecast of the annual sales 230 00:37:18,240 --> 00:37:30,540 of Babu restaurant then it will be given as Q15 as 284 into 1 plus g is 0.0718 to the 231 00:37:30,540 --> 00:37:42,570 power 15 and that is 803.436 thousand rupees. So this is a very simple example of sales 232 00:37:42,570 --> 00:38:00,510 forecast that at any time the sale QT is defined as a compounded annual growth function. 233 00:38:00,510 --> 00:38:07,220 Now we take another exercise on demand forecasting another simple example. The operations manager 234 00:38:07,220 --> 00:38:17,090 of a TV set manufacturing company believes that sales of its products in any month St 235 00:38:17,090 --> 00:38:26,500 increase by the same percentage as income It during the previous year. Write an equation 236 00:38:26,500 --> 00:38:37,230 for sales forecast. This month, sales totaled rupees 500 thousand while family disposable 237 00:38:37,230 --> 00:38:46,630 income increased from rupees 25,000 to rupees 26,000 forecast the next year's sales. 238 00:38:46,630 --> 00:38:54,500 So for the first part of the question is, write an equation for sales forecast. The 239 00:38:54,500 --> 00:39:02,530 problem statement says that the operation manager believes that the sales of its product 240 00:39:02,530 --> 00:39:12,270 in month, St increases by the same percentage as income It. So we shall write St plus 1 241 00:39:12,270 --> 00:39:23,870 as equal to St plus the change in S. The change in S as mentioned here is some fraction of 242 00:39:23,870 --> 00:39:31,510 St and that some fraction is nothing but as income percentage change. The income percentage 243 00:39:31,510 --> 00:39:36,750 change is It minus t minus 1 by It minus 1. 244 00:39:36,750 --> 00:39:47,330 This is the fractional change which is same for St. So, the expression U is the the random 245 00:39:47,330 --> 00:39:59,150 error. So St plus 1 is St plus St into this fraction which is same as now the next part 246 00:39:59,150 --> 00:40:05,900 of the question is if the values are given you just put the values here. We put 500,000 247 00:40:05,900 --> 00:40:17,510 is the St which is taken outside so it is 1 plus 26,000 and it increased from 25 to 248 00:40:17,510 --> 00:40:31,610 26 so 26 minus 25 by 25 and that resulted in a value of 520,000 rupees that is the next 249 00:40:31,610 --> 00:40:34,370 year's sales. 250 00:40:34,370 --> 00:40:44,650 So today, we have seen some applications, some exercises on basic microeconomic theory 251 00:40:44,650 --> 00:40:55,520 and also on demand forecasts. In the next lecture, we shall take some more exercises 252 00:40:55,520 --> 00:41:05,270 on production and then we switch over to cost benefit analysis, break-even analysis, and 253 00:41:05,270 --> 00:41:17,600 further in our forthcoming lectures next few lectures we shall study various aspects of 254 00:41:17,600 --> 00:41:24,470 costing, accounting, and engineering economy. Thank you very much.