Alright. When we deal with our ISO cost and ISO quant lines together, we can find the cost minimizing point where we can make a level of production for the lowest cost. Let's check it out. So the optimal combination of inputs, it reflects the lowest cost to produce a given amount of units. Right? So let's say we want to make 1,000 cookies. Well, we want to make those 1,000 cookies at the lowest possible cost. So we have a certain level of production which we'll find on our ISO quant curve, and then we'll have our costs shown on our ISO cost curve for different levels of inputs, how much that would cost us. Well, if we put those together, we can find the cost minimizing point and that cost minimizing point, it's where an ISO Quant curve is tangent to the ISO cost line. So what does that tangent mean? That means they touch at just one point. So tangent means touch at just one point. Okay. That is what they're tangent at that point. Okay. So let's go ahead and see this as an example. It's actually pretty easy to do this when we do it in an example.

Spooky Cookies bakes cookies with 2 inputs, ovens and bakers. Ovens cost $6,000 per month, and bakers cost $3,000 per month. ISO quant curves are shown for two levels of production, 5,000 and 7,500 cookies. What is Spooky's cost minimizing combination of labor and capital for 5,000 cookies? So notice they didn't label any of the curves. They didn't label our ISO quant, our ISO cost. So which one's which? Well, we know that the ISO quant curves are the ones that are curved like this. Right? The ISO quant curves are curved like this because what do they show us? They show us different levels of inputs that lead to the same amount of output. Okay. So this and which one's going to be which? These are our 2 ISO Quant, Right? This one these these right here, the blue ones are our ISO Quant curves. Right? So which one is for 5,000 and which one is for 7,500? They told us they showed us 2. So which one do you think is going to be for 5,000 and 7,500? Well, the one further away has to be the higher production. Right? Because we're going to need more inputs to make more production. So right here has to be the 5,000, cookies, and this one has to be our 7,500 cookies. Okay. So what does this tell us? We don't need that outer one. Right? We're only concerned with the 5,000 cookies. So let's go ahead and find out how do we minimize the cost to So let's go ahead and find out how do we minimize the cost to maximize the profits. So like I said, what we need to do is we need to find the ISO cost curve that is tangent to the ISO quant curve. So at any point that that this ISO quant curve, this blue curve, at the point that it just touches a budget line, that is going to be our cost minimizing point. So it's very clear where that is, and it's going to be this point right here. Right? That's the only point where they're just touching for a moment, even though they're on top of each other for a little bit, that's the exact point, right, where they're touching on top of each other. So that is the cost minimizing point to produce 5,000 cookies. Notice this point right here is not going to be cost minimizing. Why? Because we're on a further ISO cost line, those yellow lines are the ISO cost lines. So as we move further from the origin, right, as we discussed in ISO cost lines, that's a bigger budget. So an ISO cost line that's further from the origin has a higher budget. Now what about this line right here? This is a lower budget ISO cost line cannot produce 5,000. There's no point on this line, on this lower line down here that can produce 5,000 cookies because it never touches our ISO Quant line, right? The ISO Quant line shows us different combinations that can produce 5,000 cookies. The ISO cost line, here. At this point, where we produce, with 4 bakers and 2 ovens. So 4 bakers and 2 ovens is our cost minimizing point. So that is the combination of inputs that we should use to produce 5,000 cookies. Cool? Alright. Let's go ahead and pause here and then we'll discuss one more topic related to this.