Intermediate Microeconomics Sem 4 Eco(H) 2025 PYQ Q7 | CUET PG ECONOMICS COACHING

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[00:00:05]Hello Everyone, Let Us Go Ahead and Look at Question Number Seven of 2025 Paper. Look, Black Smoke Eatery Is The Only Restorer In A Small Town. They face inverse demand function and cost given. Unfortunately, the eatery produces a lot of unsightly black smoke. So that means there is an externality.

[00:00:29]So pollution is equal to q.

[00:00:32]Find the unregulated equilibrium. Suppose that the external cost of black smoke pollution is this. Find the social optima. If the regulator is to seek socially optimal output, what will be the pollution quota? If the regulator is to seek socially optimal output, what emission fee would she be asking?

[00:00:51]So, a pretty simple question. Let us start with the solution. So, this is a basic externality question that we have to solve. That's right sir. Let's start.

[00:01:10]So I think finally we have solved the entire paper now. I'll put this on the portal. You can access this from the portal. Ok? Let go.

[00:01:21]So you are given that, let me open the question paper.

[00:01:30]Yes sir you are given that P = 25 - 0.05Q and total cost is given to you as 3 + 4Q and external cost pollution is given as Q. So there will be unregulated equilibrium. Let's make MR = MC.

[00:01:58]So total revenue will be price * quantity. So 25 - 0.05q * q 25q - 0.05q² So marginal revenue will be 25 - 2 * 0.05q 25 - 0.10q And what will be the marginal cost? Differentiate the cost function four.

[00:02:32]So MR is equal to MC. So 21 = 0.1Q so Q will be 21 / 0.10 i.e. 200.

[00:02:49]Ok? This will be your equilibrium. Let's find out the price. P will be 25 - 0.05Q.

[00:02:59]So 25 - 0.05 * 210 so from here our price will come to 14.5.

[00:03:09]Ok? This has become unregulated. Now we will remove the regulated one. So we will consider the external cost. So our total cost function that will become social social cost function, social total cost function will be this total cost plus external cost, so this will become 3 + 5q and social marginal cost will become five, so now we will be equating MR to MC, right, MR to MC, this is only Q, right, external cost is given to you as Q, only right, 2Q is not given, it produces pollution equal to Q, right, let's read it.

[00:04:16]Well, it is written in the second that the external cost of black smith pollution is 2Q.

[00:04:23]Ok? So per unit a so Q units of pollution and for every pollution to is the cost. Ok? Ok. So, external cost will be 2Q.

[00:04:39]That is what I thought that somewhere I read 2q so it would become 6q. Social total cost will be 6q now. The social marginal cost will now be six. Ok? Now social total cost is nothing but private total cost plus external cost. This can be written as private marginal cost plus external marginal cost. It's six.

[00:05:03]So what was the marginal revenue? 25 - 0.1q so MR equal to social marginal cost -6 okay?

[00:05:14]So now just solve this thing will it come?

[00:05:16]So 19 = 0 a 0 1q and q will be 190 okay? Q Will Be 190. Is it clear? Have you understood this? So now if Q will be 190 then P can come out. I can just leave it to you guys. P will be 25 - 0.05Q.

[00:05:51]Ok? Just Go Ahead and Find Out This.

[00:05:57]Ok? So just put the value and get the price.

[00:06:06]You will get some answer. Ok?

[00:06:11]Let me just solve it only for you guys.

[00:06:14]Let me open the calculator.

[00:06:18]So 25 -05 * 19 is fine. So what was the price coming earlier 14.5 now the price is coming as 15.5 right? Is it clear? Is it clear?

[00:06:46]Ok? Let's see the third part. So what is the third part saying? The third part was saying that now we need to charge a tax. Right? That is the first thing that we will be charging.

[00:07:02]And second, what were we supposed to do? quota. Right?

[00:07:04]These two things were there. If the regulator seeks socially optimal output. Meaning if we have to go to 190. So what will be the quota that we will be setting pollution quota.

[00:07:14]And the second is if he sees to socially optimal output what will be the emission fee. Emission fee means one way is to find a Pigovian tax. We need to find a fee.

[00:07:25]Okay, so this is what we need to go ahead and we need to do.

[00:07:32]So let's go ahead and begin with that.

[00:07:38]So part number three, so for pollution quota, what does pollution quota mean? You decide that you cannot produce more than this. So your optimal quantity is coming at 190 na. So you will fix it at so what was pollution. What did he say? Pollution is Q units.

[00:08:05]This Is What They Said? So there if Q is 190. So pollution optimal pollution will be 190 units. So I will fix the quota at 190 so take a look graphically what it means think about it. So this is MR a MB marginal benefit curve.

[00:08:26]This is the marginal cost curve. Ok?

[00:08:29]Private. This is the marginal cost curve.

[00:08:32]Social I am making graphs generally. Not for these equations.

[00:08:37]From here I am getting 190 and from here 210 so what I am saying is that I am fixing it at 190 I have put this quota here of 190 so the quota will be at this no right is it clear this thing is understood ok now go ahead and do the last part fee wala do ok.

[00:09:09]So part number D emission fee.

[00:09:20]Ok? So now we go ahead and when we talk about emission fees, when we talk about emission fees, we are talking about a way to arrive at the socially optimal output. Ok? So we know that we have to adjust the MR in such a way that our monopolist equates the MR with the social marginal cost, only then will his equilibrium change. So we need its social marginal cost to be the private marginal cost plus the tax rate.

[00:09:55]Ok? What was his marginal revenue?

[00:09:58]21 - 0.1 times q 0.1 times q is its marginal revenue and marginal cost. What is its marginal revenue? The marginal cost was 4 and + t + t okay? So here we can say 25 - 0.1 * 190 = 4 + t marginal revenue I am equating it with marginal cost and in marginal cost I am considering the external cost. So from here when you will be solving this then you will get 6 = 4 + t then the optimal value of t will be 2.

[00:10:43]The optimal value of t will become two. Is it clear? Did you understand this?

[00:10:50]Ok? Now let us look at the second part of the question.

[00:10:54]So, one last time I will scroll up and read the last part of the question.

[00:11:06]Ok? So this is saying Babita and Rita are two individuals who are sharing an apartment in the free market. They spot a five-year-old TV that would look great in their living room. The utility function of Babita is given to you as this and the utility function of Rita is given to you as this. In these expressions MB and MR are the amount of money Babita and Rita have to spend on the other goods. TV is equal to one if they get the TV and zero if they don't.

[00:11:35]This is the whole model of public good.

[00:11:39]Ok? If This Spend Find Babitas & Ritas Reservation Price for Team. Ok?

[00:11:49]This whole question is that we did it for the public good.

[00:11:57]Chapter. The same question has been asked completely. Isn't it?

[00:12:00]We also learned how to calculate reservation prices. Let go.

[00:12:02]So let's see. So now we are talking about Babita.

[00:12:09]Watch Babita's Utility Without TV.

[00:12:13]Without TV. So I Can Write It As W TV Without TV. Meaning we will plug in the value of TV as zero. So what is the utility function given to us? What utility function is given to us? Babita's utility function is 1 + TV * MB so if TV becomes 0 then 1 + 0 * MB means this will become MB and what will be her utility function when she buys TV then the value of TV will become one.

[00:12:45]So this is with TV with TV.

[00:12:49]This is without TV. So with TV it will be 1 + 1 * MB that means 2MB that means 2MB okay but here there is an interesting thing which you have to understand that if she is buying a TV, if she is buying a TV then she won't be able to spend her entire wealth on the private good, she will not be able to spend her entire wealth on her private good, so here her entire wealth will go on the private good.

[00:13:22]So this will become 1 * MB and all the wealth will go to private goods.

[00:13:28]So our MB is the amount of private good that will be WB, the entire wealth went towards private good. But here as we are talking about this MB. This happened because we bought a TV, so after spending TV, we spent Rs. RB amount on TV. Babita spent RB amount on TV and her total wealth was WB. So WB - RB is the total wealth minus the reservation price of the private good she can buy in this case.

[00:14:03]She will be able to take that much private good. This is understandable. So basically this is the value here because she has spent RB amount on TV. He spent it on RB TV.

[00:14:15]And total is WB. So WB - RB is the remaining amount that will be spent on your private co. Ok? What are we saying now? Now we are going ahead and saying that the reservation price is the price at which you get the same utility from both.

[00:14:34]So for reservation price we need same utility from both. Same utility means that WB = 2 WB - RB so WB = 2WB - 2RB so we can say 2RB = WB RB will be WB / 2 RB will become WB / 2, did you understand this.

[00:15:08]Now the same we have to do for the other individual. You will have to do it for others too.

[00:15:12]So for that, what was the other one's name? Rita.

[00:15:15]Rita's utility function is 2 + tv * mr and Rita's wealth is wr and Rita's reservation price is RR. So when there is no TV, when there is no TV, means without TV, Rita's utility will be 2 + 0 and the entire wealth will be spent on private good wr, so this will become 2 * wr and with TV, Rita's wealth will become utility with TV, so two and the value of TV will become one and how much will you be able to spend on private good? Income of Rita minus what she gave up for TV. Which is every reservation pays. The remaining amount is all she can spend on TV. This is total wealth. Out of this, she paid the reservation price i.e. the minimum price which she could pay for the TV.

[00:16:17]So remaining she can buy private put. So this is going to be our 3 wr - r equals the two equilibrium. So 2WR = 3 Wr - RR so we can say 2WR = 3WR - 3 RR 3R = WR so RR will become WR / 3 Wr / 3 so this will be its equilibrium price that will be the reservation price.

[00:16:55]So this will be the reservation price of Vita and Babita. Is this clear? Any doubt in this? Let go.

[00:17:04]So with this we come to the end of 2025 paper. Ok? Thank you.