WEBVTT 00:00:00.040 --> 00:00:02.460 The following content is provided under a Creative 00:00:02.460 --> 00:00:03.870 Commons license. 00:00:03.870 --> 00:00:06.910 Your support will help MIT OpenCourseWare continue to 00:00:06.910 --> 00:00:10.560 offer high-quality educational resources for free. 00:00:10.560 --> 00:00:13.460 To make a donation or view additional materials from 00:00:13.460 --> 00:00:16.180 hundreds of MIT courses visit mitopencourseware@ocw.mit.edu. 00:00:22.300 --> 00:00:24.770 PROFESSOR: Hi, welcome back to the 14.01 00:00:24.770 --> 00:00:26.360 problem solving videos. 00:00:26.360 --> 00:00:29.300 Today we're going to work on p-set 1 problem 00:00:29.300 --> 00:00:31.980 number 3 from Fall 2010. 00:00:31.980 --> 00:00:33.160 And we're going to work through all four 00:00:33.160 --> 00:00:34.540 parts of this problem. 00:00:34.540 --> 00:00:38.120 But to start off I'm just going to read through part A. 00:00:38.120 --> 00:00:40.230 Consider the market for apple juice. 00:00:40.230 --> 00:00:43.120 In this market the supply curve is given by quantity 00:00:43.120 --> 00:00:48.500 supplied equals 10 pj minus 5 pa, and the demand curve is 00:00:48.500 --> 00:00:53.390 given by quantity demanded equals 100 minus 15 pj plus 10 00:00:53.390 --> 00:00:58.590 pt, where j denotes apple juice, a denotes apples, and t 00:00:58.590 --> 00:01:00.110 denotes tea. 00:01:00.110 --> 00:01:04.019 Part A asks us to assume that pa is fixed at $1 00:01:04.019 --> 00:01:06.100 and pt equals 5. 00:01:06.100 --> 00:01:08.900 We need to calculate the equilibrium price and quantity 00:01:08.900 --> 00:01:12.160 in the apple juice market. 00:01:12.160 --> 00:01:15.500 So to start off this problem, I wrote down both the supply 00:01:15.500 --> 00:01:17.120 and the demand functions. 00:01:17.120 --> 00:01:19.580 But before we get started with the algebra, I wanted to come 00:01:19.580 --> 00:01:21.530 over to this graph and I wanted to think about 00:01:21.530 --> 00:01:25.620 conceptually what we're going to be doing. 00:01:25.620 --> 00:01:28.030 When we solve for an equilibrium price and the 00:01:28.030 --> 00:01:30.840 equilibrium quantity, all we're doing is we're finding 00:01:30.840 --> 00:01:36.050 the point at which the quantity supplied and the 00:01:36.050 --> 00:01:38.200 quantity demanded is equal. 00:01:38.200 --> 00:01:41.700 Looking at the graph, that point is going to be right 00:01:41.700 --> 00:01:47.940 here where the two curves intersect. 00:01:47.940 --> 00:01:52.920 So this will be q star, our equilibrium quantity, and this 00:01:52.920 --> 00:01:57.020 will be p star, our equilibrium price. 00:01:57.020 --> 00:01:59.160 So for part A we're just solving for the equilibrium 00:01:59.160 --> 00:02:00.560 price and quantity. 00:02:00.560 --> 00:02:03.690 And they try to trip you up on this problem by throwing in 00:02:03.690 --> 00:02:06.500 the price of apples and the price of tea. 00:02:06.500 --> 00:02:09.340 But since they tell us what these prices are initially, 00:02:09.340 --> 00:02:10.830 we're just going to plug these into our supply 00:02:10.830 --> 00:02:12.250 and our demand functions. 00:02:12.250 --> 00:02:15.760 And once we do that, we'll have isolated the pj variable 00:02:15.760 --> 00:02:17.770 and the q variable so we'll be able to solve 00:02:17.770 --> 00:02:20.320 through for this problem. 00:02:20.320 --> 00:02:25.620 So starting off with part A. We're going to go ahead and 00:02:25.620 --> 00:02:29.590 we're going to set the quantity supplied equal to the 00:02:29.590 --> 00:02:31.680 quantity demanded. 00:02:31.680 --> 00:02:35.080 And so for my supply function, I've already plugged in pa. 00:02:35.080 --> 00:02:41.010 And after plugging in pa I found that 10 pj minus 5 is 00:02:41.010 --> 00:02:42.620 the supply curve. 00:02:42.620 --> 00:02:51.960 And the demand curve is equal to 150 minus 15 pj. 00:02:51.960 --> 00:02:54.460 Solving out for pj I find that the equilibrium 00:02:54.460 --> 00:02:58.200 price is equal to 6.2. 00:02:58.200 --> 00:03:00.300 And since I know this is an equilibrium price I'm going to 00:03:00.300 --> 00:03:03.400 go ahead and I'm going to label this with a star. 00:03:06.430 --> 00:03:08.880 Solving through for the equilibrium quantity all we 00:03:08.880 --> 00:03:11.950 have to do is we have to take this equilibrium price we 00:03:11.950 --> 00:03:15.390 found and plug it back into either the supply curve or the 00:03:15.390 --> 00:03:16.980 demand curve. 00:03:16.980 --> 00:03:18.500 I'm going to go ahead and I'm going to plug it into the 00:03:18.500 --> 00:03:19.750 supply function. 00:03:26.450 --> 00:03:29.740 And that lets us solve for the equilibrium quantity denoted 00:03:29.740 --> 00:03:31.150 with the star. 00:03:31.150 --> 00:03:36.180 And that in this case is 57. 00:03:36.180 --> 00:03:40.220 So looking at our graph, the equilibrium price and the 00:03:40.220 --> 00:03:42.820 equilibrium quantity, we can now label them. 00:03:42.820 --> 00:03:46.370 We can label the price, 6.2, and the 00:03:46.370 --> 00:03:53.170 equilibrium quantity 57. 00:03:53.170 --> 00:03:56.650 Let's go ahead and move on to part B. Part B is going to be 00:03:56.650 --> 00:04:00.430 the exact same scenario as we started off with in part A, 00:04:00.430 --> 00:04:03.600 only what we're going to do now is we're going to shift 00:04:03.600 --> 00:04:08.520 the supply curve by changing the price of apples. 00:04:08.520 --> 00:04:12.050 Part B states, suppose that a poor harvest season raises the 00:04:12.050 --> 00:04:14.815 price of apples to pa equals 2. 00:04:19.730 --> 00:04:22.700 Find the new equilibrium price and quantity of apple juice 00:04:22.700 --> 00:04:26.280 and draw a graph to illustrate the answer. 00:04:26.280 --> 00:04:28.620 Now what's happening in this scenario is that the demand 00:04:28.620 --> 00:04:30.080 curve is completely unaffected. 00:04:30.080 --> 00:04:31.960 The only thing that's changing is our 00:04:31.960 --> 00:04:34.350 supply curve is shifting. 00:04:34.350 --> 00:04:37.390 So when we look at our supply curve we have to think about 00:04:37.390 --> 00:04:40.030 conceptually what do apples represent. 00:04:40.030 --> 00:04:42.000 Well they're an input for the suppliers. 00:04:42.000 --> 00:04:45.090 It's something they have to use to make the apple juice. 00:04:45.090 --> 00:04:47.980 And if the price of apples is increasing then we intuitively 00:04:47.980 --> 00:04:52.180 know that this quantity, or this q star that they produce 00:04:52.180 --> 00:04:54.240 before, it's going to be more expensive for 00:04:54.240 --> 00:04:55.680 them to produce it. 00:04:55.680 --> 00:04:58.800 And, in fact, it's going to be more expensive for the 00:04:58.800 --> 00:05:03.510 suppliers to produce any given quantity. 00:05:03.510 --> 00:05:07.240 So this means that the supply curve for part B is shifting 00:05:07.240 --> 00:05:09.580 up and to the left. 00:05:09.580 --> 00:05:12.980 I'm going to denote this by labeling our new supply curve 00:05:12.980 --> 00:05:16.050 sb for Part B. 00:05:16.050 --> 00:05:18.605 So for Part B all we're going to do is we're going to plug 00:05:18.605 --> 00:05:20.460 in this new pa price. 00:05:20.460 --> 00:05:21.760 And then we're going to do the same thing. 00:05:21.760 --> 00:05:23.570 We're going to set the quantity supplied and the 00:05:23.570 --> 00:05:24.990 quantity demanded equal. 00:05:39.100 --> 00:05:43.630 When we solve through for a new supply curve we find that 00:05:43.630 --> 00:05:49.220 10pj minus 10 is our new supply curve. 00:05:49.220 --> 00:05:51.950 And we know that are demand curve is going to be exactly 00:05:51.950 --> 00:06:01.650 the same as the scenario that we started off with in Part A. 00:06:01.650 --> 00:06:04.310 Solving through for the new equilibrium price we find that 00:06:04.310 --> 00:06:10.460 pj is going to be equal to 6.4. 00:06:10.460 --> 00:06:18.650 I'm going to label this new equilibrium price with a B. 00:06:18.650 --> 00:06:21.830 And then we can take this equilibrium price, we can plug 00:06:21.830 --> 00:06:24.680 it back into either our new supply curve 00:06:24.680 --> 00:06:26.500 or our demand curve. 00:06:26.500 --> 00:06:31.800 And we can find that the equilibrium quantity is going 00:06:31.800 --> 00:06:36.630 to equal 54. 00:06:36.630 --> 00:06:40.520 And when we look at our graph we can think about what these 00:06:40.520 --> 00:06:44.490 quantities and these new prices looks like. 00:06:44.490 --> 00:06:51.060 We can see that the quantity for part B clearly should have 00:06:51.060 --> 00:06:55.130 shifted down, and it did drop from 57 to 54. 00:06:55.130 --> 00:06:59.390 And we can see that the price is higher than what 00:06:59.390 --> 00:07:00.710 we started off with. 00:07:00.710 --> 00:07:06.000 It rose from 6.2 now up to 6.4. 00:07:06.000 --> 00:07:08.010 So we can see that our intuition that the supply 00:07:08.010 --> 00:07:10.340 curve would shift up because it's more expensive for 00:07:10.340 --> 00:07:13.320 suppliers makes sense according to both our algebra 00:07:13.320 --> 00:07:14.570 and to our graph. 00:07:16.520 --> 00:07:19.720 Let's go ahead and try part C. Part C is going to be another 00:07:19.720 --> 00:07:22.560 shift, but what's happening now is this new shift is going 00:07:22.560 --> 00:07:24.780 to affect the demand curve not the supply curve. 00:07:28.090 --> 00:07:33.040 Part C states, suppose that pa equals 1, but the price of tea 00:07:33.040 --> 00:07:35.560 drops to pt equals 3. 00:07:35.560 --> 00:07:40.470 Find the new equilibrium price and quantity of apple juice. 00:07:40.470 --> 00:07:45.120 So for this scenario now, our pa is back to 1, like it 00:07:45.120 --> 00:07:49.240 started off with in part one. 00:07:49.240 --> 00:07:55.820 But now t is dropped from five to three. 00:07:55.820 --> 00:07:58.020 Now before we start, let's think about what t actually 00:07:58.020 --> 00:08:01.780 represents to the consumers in this market. 00:08:01.780 --> 00:08:04.100 If I'm a consumer and I'm debating what I want to drink 00:08:04.100 --> 00:08:07.330 in the morning, one of my other choices might be tea. 00:08:07.330 --> 00:08:10.540 Now the price of tea drops, then maybe I'll be less 00:08:10.540 --> 00:08:12.640 willing to pay as much for the apple juice because they can 00:08:12.640 --> 00:08:15.340 just go out and get the cheap tea now. 00:08:15.340 --> 00:08:18.820 Looking at our graph, if the consumer is less willing to 00:08:18.820 --> 00:08:22.020 pay as much for each quantity of apple juice as they were 00:08:22.020 --> 00:08:26.120 before, this scenario means that the demand curve has 00:08:26.120 --> 00:08:28.160 shifted down. 00:08:28.160 --> 00:08:31.320 So, for example, the equilibrium quantity that we 00:08:31.320 --> 00:08:34.580 started off with an point A, they used to be willing to pay 00:08:34.580 --> 00:08:37.179 this much, now they would only be willing to pay this much 00:08:37.179 --> 00:08:41.230 for the same quantity because tea is cheaper. 00:08:41.230 --> 00:08:44.110 Now we're going to be using the same supply curve that we 00:08:44.110 --> 00:08:45.880 started off with before. 00:08:45.880 --> 00:08:49.870 So in this scenario we're looking to set supply and 00:08:49.870 --> 00:08:52.470 demand equal and find this new equilibrium point. 00:08:57.480 --> 00:09:00.330 When we go through and we actually plug in the new pa 00:09:00.330 --> 00:09:05.630 and the new pt, we're going to find that the supply and the 00:09:05.630 --> 00:09:06.880 demand functions. 00:09:15.410 --> 00:09:22.000 When we set them equal we're going to set 10 pj minus 5 00:09:22.000 --> 00:09:36.360 equal to 130 minus 15 pj. 00:09:36.360 --> 00:09:39.640 Again we're going to solve through for pj. 00:09:39.640 --> 00:09:43.190 And we're going to find that our pjc for part C is going to 00:09:43.190 --> 00:09:44.440 be equal to 5.4. 00:09:47.030 --> 00:09:50.000 And we're going to find that the new equilibrium quantity, 00:09:50.000 --> 00:09:52.470 again either plugging back into our supply curve or 00:09:52.470 --> 00:10:02.860 demand curve, is going to be equal to 49. 00:10:02.860 --> 00:10:06.410 And when we think back to our original part A, we found that 00:10:06.410 --> 00:10:08.430 the price was 6.2. 00:10:08.430 --> 00:10:13.030 Now the price dropped down to 54 or 5.4. 00:10:13.030 --> 00:10:16.190 And what we see here, is that we did see a price decrease, 00:10:16.190 --> 00:10:17.840 or we could have predicted a price decrease 00:10:17.840 --> 00:10:19.480 according to our graph. 00:10:19.480 --> 00:10:22.610 And we also find out the quantity dropped from part A 00:10:22.610 --> 00:10:25.670 in 57 now the 49. 00:10:25.670 --> 00:10:27.460 And according to our graph, we would have predicted that 00:10:27.460 --> 00:10:30.510 quantity would have decreased as well. 00:10:30.510 --> 00:10:34.530 So the algebra and our graph both match up. 00:10:34.530 --> 00:10:38.180 Let's go ahead and move on to part D. Now we're going to 00:10:38.180 --> 00:10:40.980 look at the effect of a government intervention on the 00:10:40.980 --> 00:10:43.920 market for apple juice. 00:10:43.920 --> 00:10:49.640 Part D says, suppose that pa equals 1 and pt equals 5 and 00:10:49.640 --> 00:10:51.590 there's a price ceiling on apple juice of 00:10:51.590 --> 00:10:54.050 pj star equals 5. 00:10:54.050 --> 00:10:57.470 What is the excess demand for apple juice as a result? 00:10:57.470 --> 00:11:01.480 Draw a graph to illustrate your answer. 00:11:01.480 --> 00:11:03.790 So now we're back to the original scenario we started 00:11:03.790 --> 00:11:09.435 with in part A. We have the price of apples is equal to 1. 00:11:09.435 --> 00:11:15.600 And we're back to the price of tea equal to five. 00:11:18.240 --> 00:11:21.270 And now the only thing that's different in this scenario for 00:11:21.270 --> 00:11:30.330 part D is that the government said that these suppliers 00:11:30.330 --> 00:11:35.820 can't charge any price higher than 5. 00:11:35.820 --> 00:11:38.100 So let's go ahead and let's think about what this looks 00:11:38.100 --> 00:11:40.280 like conceptually on a graph. 00:11:57.280 --> 00:11:59.680 In this scenario we started off with an 00:11:59.680 --> 00:12:01.210 equilibrium price of 6.2. 00:12:06.140 --> 00:12:07.810 If we were to have a case where the government was 00:12:07.810 --> 00:12:12.450 saying you could charge only as much as 7 in the market for 00:12:12.450 --> 00:12:15.160 apple juice, the suppliers wouldn't even be affected. 00:12:15.160 --> 00:12:17.580 Because they would say, that doesn't affect us, we're 00:12:17.580 --> 00:12:19.400 charging 6.2. 00:12:19.400 --> 00:12:21.170 That's too high. 00:12:21.170 --> 00:12:23.300 We're not going to have to change anything we're doing. 00:12:23.300 --> 00:12:25.940 But in this scenario the government is saying the most 00:12:25.940 --> 00:12:27.940 you can charge is 5. 00:12:36.150 --> 00:12:40.670 Now at the price of 5, the quantity supplied, or the 00:12:40.670 --> 00:12:45.100 intersection of the price of 5 with the supply curve, is 00:12:45.100 --> 00:12:53.420 going to lead to a qs that's different than the quantity 00:12:53.420 --> 00:12:54.670 that's demanded. 00:12:56.810 --> 00:12:58.880 And more specifically we're going to find that too many 00:12:58.880 --> 00:13:01.650 people are demanding the product and there's not enough 00:13:01.650 --> 00:13:03.810 being supplied in the market. 00:13:03.810 --> 00:13:06.430 This is what we're referring to when we talk 00:13:06.430 --> 00:13:09.340 about excess demand. 00:13:09.340 --> 00:13:12.140 We're talking about the space between the quantity that's 00:13:12.140 --> 00:13:14.650 supplied and the quantity that's demanded. 00:13:14.650 --> 00:13:16.900 And that's what we're going to be solving for. 00:13:16.900 --> 00:13:20.650 So by plugging in the price cap of 5 into both our supply 00:13:20.650 --> 00:13:23.420 curve and our demand curve, we'll be able to find the 00:13:23.420 --> 00:13:25.710 difference between the amount that's supplied and the amount 00:13:25.710 --> 00:13:26.960 that's demanded. 00:13:29.890 --> 00:13:34.910 So plugging into our supply curve we can find that the 00:13:34.910 --> 00:13:45.010 quantity supplied is going to be equal to 45. 00:13:45.010 --> 00:13:48.410 And plugging into our demand curve we can find that the 00:13:48.410 --> 00:14:00.680 quantity demanded is going to be equal to 75. 00:14:00.680 --> 00:14:02.450 Now one of the biggest problems that students run 00:14:02.450 --> 00:14:04.440 into on this problem is they think they're done when they 00:14:04.440 --> 00:14:05.710 reach this point. 00:14:05.710 --> 00:14:08.150 All right, I found the quantity supplied, I found the 00:14:08.150 --> 00:14:09.780 quantity demanded, I know they're different. 00:14:09.780 --> 00:14:11.120 I'm done. 00:14:11.120 --> 00:14:14.760 But really what you need to find is exactly how different 00:14:14.760 --> 00:14:17.630 the quantity supplied and the quantity demanded is. 00:14:17.630 --> 00:14:19.210 You need to find out how many consumers are 00:14:19.210 --> 00:14:20.460 left out of the market. 00:14:38.370 --> 00:14:40.300 So our excess demand is the difference between the 00:14:40.300 --> 00:14:42.870 quantity supplied and the quantity demanded. 00:14:42.870 --> 00:14:45.130 And that's going to be 30 in this case. 00:14:45.130 --> 00:14:48.270 So just to review what we did in this problem, we started 00:14:48.270 --> 00:14:51.770 off by setting a quantity supplied and a quantity 00:14:51.770 --> 00:14:53.790 demanded equal to solve for a basic 00:14:53.790 --> 00:14:55.770 equilibrium price and quantity. 00:14:55.770 --> 00:14:58.150 We then looked at shifts in supply and demand and looked 00:14:58.150 --> 00:15:00.950 at how that affected the price and quantity in a market. 00:15:00.950 --> 00:15:03.630 And finally, we ended with part D with looking at the 00:15:03.630 --> 00:15:05.570 effect of a government intervention. 00:15:05.570 --> 00:15:08.770 How does a price cap affect how many people can get a 00:15:08.770 --> 00:15:11.140 product compared to how many people want a product.