Consumer Optimum Consumption: Budget Constraint and Indifference Curves

Alright. So now let's put together the ideas of the budget constraint and our indifference curves to find the consumers optimum consumption. So the consumers optimum consumption. This is gonna be where the consumer gets the maximum amount of utility, right? They want to get as much satisfaction, as much utility within their budget, right? They're only gonna have so much money to get as much utility as possible out of it. Okay, so when we talk about optimum consumption with indifference curves and budget constraints, it's gonna be the point where an indie difference curve is tangent to the budget constraint. Okay, so tangent, it's this mathematical concept and that's where they touch only they touch only at one point at one point. Okay, so they only touch at one point you're gonna have an indifference curve and a budget constraint that they just touch at one point and that's gonna be that optimum consumption right? Where they touch. Okay, so let's go back to our example of party boy paul and wrap this all up together in one. So party boy paul, we're going back to a situation where his income was $24 vodka was selling for $6 and beer was selling for three. Alright, so we've got an income of 24 vodka selling for six. And beer selling for three. Okay. And what we did is we had found out previously we had graphed his utility or his indifference curves, right? For levels of 500 utility right here 750 utility out here, right? And then what we also have is his budget constraint which we also figured out to be this line right here is going to be his budget constraint. Okay, so we've got it all on one graph now, so it should be pretty easy for you at this point to pick out what his optimum consumption is gonna be based on his constraint of his budget. Well, it's going to be right here at at the tangent, right? This is the only point where this utility curve touches the budget constraint. Okay. And that is going to be the optimum consumption because we're getting the most utility. We're on the furthest out utility curve that is affordable in our budget Of course, party boy Paul would prefer this other curve. Right? He would prefer to be on this 750 utility curve. There's more satisfaction there, but he can't afford it. No part of his budget touches that 750 utility curve, so it is not affordable for him. None of those options are affordable. But what about a situation like this? If I were to draw another curve down here. What about this curve that I just drew? It crosses? It crosses his budget constraint right there, doesn't it? But this is going to have less utility, right? Because it's closer to the origin. It's lower than the 500 utility point. So this isn't his ideal situation. Right? He would say in this, in this case, maybe he's only getting 250 utility from this graph, right? So he doesn't want to be on that curve, He wants to be on the furthest out curve with the most satisfaction and that's gonna be the 500 utility curve right there where they're tangent. Okay, so that is going to be his optimum consumption, where the indifference curve touches the budget constraint. Alright, so let's real quick, let's see how a change in income or a change in the price of the good can affect our optimum consumption. Alright, so we've seen how the change in income or change in price of good, how that affects our budget constraint. Right? And what what what's gonna happen is since we have a different budget constraint, we're gonna have a different optimum consumption. So let's see this first example where we're gonna have a change in income, let's say party boy paul makes even more money now and his income increases. What we saw when there's an increase in income, he's going to shift outward, right? We're gonna see that the line shifts outward and he might be in a situation something like I don't know, let's go I wanted to touch this curve. So I'm gonna do something like this too far. There you go. Something like that would be his new budget constraint. Now I didn't drop perfect cause it should be parallel to the other one. Um But the idea is that it's moved out, right? Because he's making more money, I'll try it one more time. I don't I don't I don't like how that. So let's try one more here. Okay let's say that that touch that was almost parallel. So you can imagine it's almost touching there. And this could be that point, right? That would be the point of his new optimum consumption where his previous optimum consumption was somewhere around there. Right? So we moved our income so we can move to a new utility curve. And you can imagine if we had a decrease in income, if we had something like this where income went down here? Well, we would have to find a new utility curve down here that's touching Excuse me, New indifference curve that's touching our lower income, right? So the whole key there is just to find the utility curve that is just touching the budget constraint at one point, right? And remember that these two are not all of our indifference curves, there's indifference curves in between here. There's all indifference curves for different levels of utility everywhere, Every little marginal bit of utility, there can be more uh more indifference curves there. Okay, So even if it wasn't touching one of these, we could find a new utility curve that it was touching. Alright, so that is how the change in income can affect it. Right? We shifted our income out and we ended up on a different utility curve now, what about the change in the price of a good, let's say now the price of vodka goes down and we can afford way more vodka. Well, remember what's gonna happen is that the vodka side's gonna change? But the beer stays constant, right? The price of the beer is the same, the income is the same, so that's not gonna move, but the vodka side will move and since we can afford more, it's gonna move out this way. Okay. So we might end up in a situation where a new budget constraint might look something like this, right? Where we still have the same point down here, but now we've got a new point up here and we have our new optimum quantity somewhere around there where it's just touching and it's tangent just at one point. So this is the new optimum on both graphs. New optimum. Okay, so the shifting of the budget constraint leads us to move to a different indifference curve or to a different point. Right? So we just gotta find where we're gonna have that tangent C condition and that will be our optimum consumption. Cool, Alright, let's go ahead and move on to the next video