Cost-Minimizing Combination of Labor and Capital - Online Tutor, Practice Problems & Exam Prep

To minimize production costs, firms identify the cost-minimizing point where the ISO quant curve (representing different input combinations for a specific output) is tangent to the ISO cost curve (indicating budget constraints). For example, a bakery producing 5,000 cookies may find that using 4 bakers and 2 ovens is optimal. Different countries have varying input costs, leading to distinct cost-minimizing combinations, such as more ovens in the USA versus more bakers in China, illustrating the concept of comparative advantage.

Cost Minimizing Combination of Labor and Capital

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.

Differences in Cost Minimizing Point

So let's extend this idea to comparative advantages in different countries. Different countries might have different costs for the different inputs. We might say that in the USA, we have a lot of capital and the capital, like the ovens, might be cheap to get, but the cost of labor to hire someone might be much more compared to China, where maybe getting ovens might be expensive and hiring more people is relatively cheaper. Right? This is just an example, but the ideas are that different countries are going to have different costs for the capital and the labor. So they'll have different cost-minimizing points. Notice what's happening here. In the USA, we can afford more ovens, and over here in China, they can afford more bakers. Right? So it gives us different ISO cost curves. The ISO cost curves are different because the prices of the different inputs are different. That leads to different cost-minimizing points. So in our example here, we would have for this level of production in the USA, maybe the cost-minimizing point would be 4 ovens and 2 bakers. Right? Just like we see here, 4 ovens and 2 bakers. Whereas for the same level of production in a different economy, well, theirs might be over here where they have 2 ovens and 4 bakers. Right? For the same level of production. Okay? So that could lead to different total costs in different countries. Cool? That's about it for this discussion. Let's go ahead and move on to the next video.

Here’s what students ask on this topic:

What is the cost-minimizing combination of labor and capital?

The cost-minimizing combination of labor and capital is the point where the ISO quant curve, representing different input combinations for a specific output, is tangent to the ISO cost curve, which indicates budget constraints. At this point, the firm can produce a given level of output at the lowest possible cost. For example, if a bakery wants to produce 5,000 cookies, it might find that using 4 bakers and 2 ovens is the optimal combination. This point ensures that the firm is using its resources most efficiently to minimize production costs.

How do ISO quant and ISO cost curves help in cost minimization?

ISO quant and ISO cost curves are essential tools in cost minimization. The ISO quant curve shows different combinations of inputs (like labor and capital) that produce the same level of output. The ISO cost curve represents the total cost for different combinations of these inputs. The cost-minimizing point is where the ISO quant curve is tangent to the ISO cost curve, meaning they touch at just one point. This tangency point indicates the most cost-effective combination of inputs to produce a specific output level, ensuring the firm operates efficiently within its budget constraints.

Why do different countries have different cost-minimizing combinations of inputs?

Different countries have varying costs for labor and capital, leading to different cost-minimizing combinations of inputs. For instance, in the USA, capital (like ovens) might be cheaper, while labor (bakers) is more expensive. Conversely, in China, labor might be cheaper, and capital more expensive. These differences result in distinct ISO cost curves and, consequently, different cost-minimizing points. For the same level of production, the USA might use more ovens and fewer bakers, while China might use more bakers and fewer ovens. This variation illustrates the concept of comparative advantage, where countries optimize production based on their relative input costs.

How do you find the cost-minimizing point on a graph?

To find the cost-minimizing point on a graph, you need to identify where the ISO quant curve is tangent to the ISO cost curve. The ISO quant curve represents different combinations of inputs that produce the same output, while the ISO cost curve shows the total cost for various input combinations. The tangency point, where these curves touch at just one point, indicates the optimal combination of inputs that minimizes production costs. For example, if a bakery's ISO quant curve for 5,000 cookies is tangent to an ISO cost curve at the point where it uses 4 bakers and 2 ovens, this is the cost-minimizing combination.

What is the significance of the tangency point between ISO quant and ISO cost curves?

The tangency point between ISO quant and ISO cost curves is significant because it represents the cost-minimizing combination of inputs for a given level of output. At this point, the firm can produce the desired output at the lowest possible cost. The ISO quant curve shows different input combinations that yield the same output, while the ISO cost curve indicates the total cost for these combinations. The tangency point ensures that the firm is using its resources most efficiently, balancing the cost of labor and capital to achieve optimal production within budget constraints.