Alright, so now let's consider how we can optimize consumption when we're thinking about utility and marginal utility. We can say that a consumer's optimum consumption represents the maximum utility. We want to get the most utility possible within our budget, right? We're going to have our budget constraint, but we want to get as much utility as we can out of that amount of income, okay? So when we think of optimum consumption and we're dealing with utility and marginal utility, we're going to see that the optimum per dollar spent is equal for both goods. We want equal marginal utility per dollar for both goods. So we're going to think about marginal utility per dollar because different goods have different prices, right? If we're going to spend more on something that brings more utility, we have to consider how much extra we spent for that, right? So we want to go by a per dollar basis, how much utility we get. So let's talk about Breakfast Bill. He spends all his income, $10, on eggs and coffee. Eggs cost $2, coffee costs $1, right? $10 of income, eggs cost 2, coffee costs 1, and then he's got some marginal utilities. These numbers would have to be given to you. There's no way you would know what Breakfast Bill's marginal utility would be from eating eggs and drinking coffee, okay? So these numbers have to be given to you. What is the optimum consumption? So we've got a different number of eggs and then different marginal utility and notice what's happening. As he eats more and more eggs, the quantity of eggs is increasing, that marginal utility decreases. Right? And that's what we would expect, the diminishing returns. As you eat more and more, those last units aren't providing as much satisfaction. The price for the eggs was $2. So let's find a marginal utility per dollar. That first egg cost us $2, but it brought 20 marginal utility.

So per dollar, we got 20∕12 marginal utility. How about the next one? When we have 16 marginal utility, well, 16∕12 and we spent an extra $2 to get that egg. We're calculating it as 8∕12 marginal utility per dollar, right? And we're not combining. It's not 4 total dollars for 2 eggs, it's 2 extra dollars for the second egg when we already have 1 egg. Let's continue for each subsequent egg: 10∕12, 6∕12, 2∕12, and 1∕12 marginal utility per dollar for eggs. Let's do the same thing with coffee, but remember the price of coffee is $1, right? So we're just going to be dividing by 1 in all these cases, so the marginal utility per dollar is just equal to the marginal utility because the price is $1, right? It would be 20, 15, 10, etc.

Now, remember what I said, optimum consumption, it's going to be where marginal utility per dollar is equal for both goods. So where do we see marginal utility per dollar equal for both goods? Here's one where this one is 10 and this one is 10. So an optimum consumption would be 1 egg and 3 coffees, right? But there are other ones. Look at this one right here, 3 eggs and 4 coffees is also another situation where we reach optimum consumption and another one here, right? 4 eggs and 5 coffees also does that for us. So notice in all these situations, we are going to be able to maximize our utility, but it depends on our income. What can we afford? Which of these packages can we afford with our $10 income? So what I want to do first is show you how this package, this best scenario package, is going to be our optimum consumption by showing you some other consumption bundles.

Let's start here where we have 5 eggs and 0 coffee and this is something we can afford. 5 eggs times the $2 cost, that's $10, right? We can afford that within our income budget. So how much utility would we get from those 5 eggs? Well, we would get 20 from the first one, Right? The marginal utility right here. This would be what we would get. The first one, we'd eat 1 egg and have 20 utility, then we'd get another 16, we'd get another 10, another 6, and another 2. Alright. So how much is this? This is going to be 36, 46, 54. How about if he gives up one of those eggs and he gets some coffee? So we're still going to be in a situation where we are spending all our income. 4 eggs times $2 is 8, plus 2 coffees times $1 is 2, 8 +2, we're still spending all our money. So let's see how much utility we get from this package. So in this case, we're going to have 4 eggs and 2 coffees. So let's see what we get. We're going to get 20 plus 16 plus 10 plus 6 from the eggs and then from the coffee, we're going to get 20 plus 15. Alright. So that's going to be our utility there, and let's see what we get. 36, 46, 52, 72 oh man, this is really pushing my mental math right now. 87. If we have 3 eggs and 4 coffees, we are at our optimum consumption for this level of income. And we just so happen to be at the right level of income here, right? We're going to have 3 eggs times $2 plus 4 coffees times $1. Well, 3 times 2 is 6 plus 4 is 10, alright? So we're still spending all of our income. Now let's see how much utility we get in this case. So 3 eggs, we're going to have 20 plus 16 plus 10, and 4 coffees. So we're going to get 20, plus 15, plus 10, plus 5. So how much utility is this? This one's going in the calculator. So 20 plus 16 plus 10 plus 20 plus 15 plus 10 plus 5. 96. I hope I did that right because I used the calculator that time. So notice 96 that is more utility than all these other packages. If you tried other combinations of eggs and coffee within the $10 limit, you would see that this is the maximum amount and that's because the marginal utility per dollar is equal in this case. Alright, so just to reiterate, notice here when we have one egg and 3 coffees, this would be a budget of 1 egg being 1 times $2 plus 3 times $1, well this would be a budget of $5 here. 2 plus 3 is $5 and when we had 1 egg notice that was this situation, 1 egg and 3 coffees. That is an optimum consumption. When we have $5 that would be what we would want to consume. Let's do the same thing with 4 eggs and 5 coffees, Right, this was where at 4 eggs, we had 3 marginal utility per dollar, 5 coffees, 3 marginal utility per dollar. Let's see how much this costs. 4 times the $2 plus 5 times $1. Right? That's going to be 8 plus 5, $13. So if we had $13 in our budget, that would be our optimum consumption bundle right there with 4 eggs and 5 coffee. So that's going to be the clear-cut way, you do the marginal utility per dollar and you find where they're equal for both goods. Alright? And just see if it's purchasable within your budget. Alright, cool. Let's go ahead and move on to the next video.