Understanding Cost Analysis in Production

As we've seen in our example from Sam's Sweater Factory, there's two types of costs that firms will face, fixed cost and variable cost. The two together sum to the total cost for a firm. Fixed costs are ones that do not change as the quantity of output is produced. In other words, for Sam's Sweater Factory, we saw that the cost of the factory remained the same regardless of the number of workers Sam hired or the amount of output the workers produced. Variable costs, on the other hand, are ones that do change with the quantity of output produced. Labor cost is our variable cost for Sam's sweater factory. As he hires more workers, he incurs more costs. We can use fixed and variable costs and total cost to come up with a couple other measurements of cost that will be important for firms to analyze as they make their profit-maximizing decision. First is average cost. Average costs take any of our cost and divide it equally across the quantity that we produce. In other words, we take fixed cost divided by quantity to find our average fixed cost, variable cost divided by quantity to find average variable, and total divided by quantity to find average total. Again, these are taking all of our cost and dividing them equally across all the units that we produce. Marginal cost goes back to the principle of marginal thinking. How much additional cost do we incur from making one additional unit of output? In other words, what's the change in total cost as we change production by one unit? What's the amount of cost that we incur just to make that one additional unit? Remember, economists make decisions at the margin. So this is going to be a key concept that's going to drive our ability to determine profit maximization. and later modules. When we look at these different types of costs, we can apply these to Sam's Sweater Factory. We know that as our output increased from hiring more and more workers, our fixed costs remain the same. And we see that regardless of the number of units of output that we produce in the first column here, fixed costs remain identical. You don't sum them in this case, but instead you pay the same regardless. Variable costs, on the other hand, are a function of the number of workers, or input, that we provide. One worker cost us $20, two workers cost us $20 each for a total of 40, three workers cost us $20 each for a total of 60, and so on. Total cost, of course, being the sum of our fixed and our variable cost added together. In order to get our averages, we take our quantity. Remember quantity is just another word for output. So in order to determine average fixed cost, we'll take each of our costs and divide them by quantities. As you can see in the table, the average fixed, average variable, and average total don't exist for a quantity of zero because we can't divide by zero. But when we go to a production of 50, we can begin calculation of these average costs. So for an output of 50, we take our total fixed cost of $100, and divide it by our quantity of 50 to get an average fixed cost of 2. To go to the next value, $100 divided by 105 gives me 95 cents, and so on. Notice the pattern for average fixed cost. It's always going down. It's always going down because we have the same cost on the top and we're dividing by an ever increasing quantity on the bottom. So average fixed cost will always be decreasing. And again, the idea here is that fixed costs are fixed, and therefore, as quantity increases, that ratio is just going to get smaller and smaller. What about average variable? Notice in average variable here, we're going to take our variable cost, so begin at a variable cost of 20, divide by the output of 50, and you get an average variable cost of 0.4. or 40 cents per unit. As we go to 105 units, variable cost increases to 40, so 40 divided by 105 gives me the.38, and so on and so on. Let's look at what's going on with variable cost, average variable cost in particular. It begins at.4, and then it falls to.38, and then it begins to increase again. Before we make any conclusions, let's look at our last average cost. Average total cost. Average total cost again reflects total cost divided by quantity. So for a quantity of 50, total cost is 120. 120 divided by 50 gives me 2.4. As we go to an output of 105, fixed cost is still the same, variable cost is rising, total cost 140. 140 divided by 105 gives me 1.33. And so on for the rest of our values. Notice here what happens with average total. It falls from 50 to 105, 2.4 to 1.33. It falls a little more, falls a little more. But as we go from 175 units to 180 units, average total cost begins to rise again. In other words, average total cost falls, but at some point it begins to rise again. The question is why? What's going on that's causing this initial decrease and then the initial rise? In order to answer that question, we have to go back to our other two average costs. Remember, average fixed and average variable come from fixed and variable cost. For any given quantity, we can also add average fixed and average variable to get average total. In other words, for a quantity of 50, 2 plus.4 gives me 2.4, and so on. So that means that the. What's going on with average total is a reflection of average fixed and average variable. Well, we see that average fixed is always falling. Average variable initially falls, but then starts to rise again. So this will help us explain what's going on with average total. Initially, average total cost falls significantly from 2.4 to 1.33. That can be explained by the fact that average fixed cost falls so significantly in the beginning. while average variable only falls a little bit. As we go from 105 to 145 units, average fixed cost still falls, but average variable cost starts to rise, but by only a small amount, and so average total still continues to fall. As we go from 145 to 175 units, average fixed still falls, but it's not falling as fast. It's starting to slow down. It's starting to taper off as we produce more output. But average variable is starting to rise by a little bit more. But we're still seeing that decrease in our average total from 1.1 to 1.03. Finally, as we go from 175 to 180 units, average fixed cost only falls by a penny. But now average variable cost increases by 10 cents. And so the net result... is we start to see a rise in our average total cost. So average total cost will always initially fall and then start to rise again. What about the last cost, marginal cost? The additional cost that we incur to produce just one more unit. As we go from 0 to 50 units, we incur 0.4 cents or 40 cents in additional cost. When we go from 50 to 105, marginal cost continues to fall. But when we get to 145 units, marginal cost starts to rise. This follows the same pattern that we saw for our average variable cost. An initial dip and then an ultimate rise. Well, remember where our costs are coming from, in particular from variable costs. They're coming from our wages. And in marginal cost, we're asking the question, how much more cost do we incur to make one more unit? But the key concept here is what are our inputs doing? In other words, what's the marginal product of production and how much are we getting out of it? When we consider how that relates to cost, these relationships are clearly explained. As we hire more and more workers, at least initially, one worker to two worker in Sam's factory was more productive, and therefore his average variable cost and average mark. and marginal cost fell. But as he hired that third worker, remember we reached diminishing marginal returns, meaning that we weren't getting as much output even though we were paying the same costs. Therefore, spreading that across all the units, costs start to rise from 0.38 to 0.41 for average variable or from 0.36 to 0.5 for marginal costs. In other words, these costs ultimately rise because of the concept of diminishing marginal product. Diminishing marginal product is going to be the driver for a lot of these cost concepts. In other words, it's going to be the driver that ultimately forces up the cost of production for any firm. If we graph these individual cost curves for SAM, what we see is some of those relationships in action. As you can see here, remember your average fixed cost is always falling and you can see that in the orange line in the graph. The green line reflects your average variable cost. As we begin to see more and more cost incur, we're going to see more and more average variable cost. And you can see it's relatively flat, but it does start to rise. Your yellow is going to reflect your average total cost. So your average total cost reflects the sum of both your average fixed in orange and your average variable in blue. Finally, or I'm sorry, average variable in green. The blue reflects your marginal cost, the ultimate rise in cost, and substantial one at that. There's some key relationships and key traits of these graphs that we can include. First, we said that average fixed cost is always falling. It's always falling because you're taking a number that never changes in the numerator of your ratio and always increasing the bottom. Average fixed costs, therefore, will always be decreasing for any type of production. But it is important to note that the value will never become zero. It may get very, very small, but it will never become zero. Second, marginal cost is always going to intersect at the minimum of the average total cost curve. This is conceptually what's known as the minimum efficient scale, or sometimes just called the efficient scale. The marginal cost also intersects the minimum of your average variable cost, but that's less important for us right now. The key idea is that because average total cost initially decreases, but then starts to increase again, we're going to see that same relationship for marginal cost as well. Marginal cost will initially fall, then rise, and all of these are being driven by this idea of diminishing marginal product. So we could generalize our cost curves with these key traits, and we could see that your typical set of cost curves is going to look something like this. Average fixed cost is always falling, and so that's very easy to identify. Your average fixed cost is here. We know that our average variable cost is an additional cost that's incurred, but it's going to initially dip and then rise again. But it can never be as... as much as average total because average fixed and average variable have to sum to meet average total. So my average variable cost will be here and average total cost here. Finally we know from our traits that your marginal cost will always intersect the average variable cost at its minimum and the average total cost at its minimum. And so this graph reflects marginal cost. These typical sets of cost curves will help us to analyze and understand the profit maximizing decision for the different types of firms that we face. Remember, as said before, all firms face the same sorts of costs. All firms have to hire workers. All firms have to buy materials. All firms face time constraints. So all firms are going to face these challenges and all firms are going to face the issue of diminishing marginal product, the ultimate driver of rising costs.

Variable costs, on the other hand, are ones that do change with the quantity of output produced. Labor cost is our variable cost for Sam's sweater factory. As he hires more workers, he incurs more costs. We can use fixed and variable costs and total cost to come up with a couple other measurements of cost that will be important for firms to analyze as they make their profit-maximizing decision. First is average cost.

Average costs take any of our cost and divide it equally across the quantity that we produce. In other words, we take fixed cost divided by quantity to find our average fixed cost, variable cost divided by quantity to find average variable, and total divided by quantity to find average total. Again, these are taking all of our cost and dividing them equally across all the units that we produce.

Marginal cost goes back to the principle of marginal thinking. How much additional cost do we incur from making one additional unit of output? In other words, what's the change in total cost as we change production by one unit?

What's the amount of cost that we incur just to make that one additional unit? Remember, economists make decisions at the margin. So this is going to be a key concept that's going to drive our ability to determine profit maximization. and later modules.

When we look at these different types of costs, we can apply these to Sam's Sweater Factory. We know that as our output increased from hiring more and more workers, our fixed costs remain the same. And we see that regardless of the number of units of output that we produce in the first column here, fixed costs remain identical.

You don't sum them in this case, but instead you pay the same regardless. Variable costs, on the other hand, are a function of the number of workers, or input, that we provide. One worker cost us $20, two workers cost us $20 each for a total of 40, three workers cost us $20 each for a total of 60, and so on.

Total cost, of course, being the sum of our fixed and our variable cost added together. In order to get our averages, we take our quantity. Remember quantity is just another word for output.

So in order to determine average fixed cost, we'll take each of our costs and divide them by quantities. As you can see in the table, the average fixed, average variable, and average total don't exist for a quantity of zero because we can't divide by zero. But when we go to a production of 50, we can begin calculation of these average costs. So for an output of 50, we take our total fixed cost of $100, and divide it by our quantity of 50 to get an average fixed cost of 2. To go to the next value, $100 divided by 105 gives me 95 cents, and so on.

Notice the pattern for average fixed cost. It's always going down. It's always going down because we have the same cost on the top and we're dividing by an ever increasing quantity on the bottom.

So average fixed cost will always be decreasing. And again, the idea here is that fixed costs are fixed, and therefore, as quantity increases, that ratio is just going to get smaller and smaller. What about average variable? Notice in average variable here, we're going to take our variable cost, so begin at a variable cost of 20, divide by the output of 50, and you get an average variable cost of 0.4. or 40 cents per unit.

As we go to 105 units, variable cost increases to 40, so 40 divided by 105 gives me the.38, and so on and so on. Let's look at what's going on with variable cost, average variable cost in particular. It begins at.4, and then it falls to.38, and then it begins to increase again. Before we make any conclusions, let's look at our last average cost. Average total cost.

Average total cost again reflects total cost divided by quantity. So for a quantity of 50, total cost is 120. 120 divided by 50 gives me 2.4. As we go to an output of 105, fixed cost is still the same, variable cost is rising, total cost 140. 140 divided by 105 gives me 1.33. And so on for the rest of our values.

Notice here what happens with average total. It falls from 50 to 105, 2.4 to 1.33. It falls a little more, falls a little more.

But as we go from 175 units to 180 units, average total cost begins to rise again. In other words, average total cost falls, but at some point it begins to rise again. The question is why? What's going on that's causing this initial decrease and then the initial rise?

In order to answer that question, we have to go back to our other two average costs. Remember, average fixed and average variable come from fixed and variable cost. For any given quantity, we can also add average fixed and average variable to get average total.

In other words, for a quantity of 50, 2 plus.4 gives me 2.4, and so on. So that means that the. What's going on with average total is a reflection of average fixed and average variable. Well, we see that average fixed is always falling.

Average variable initially falls, but then starts to rise again. So this will help us explain what's going on with average total. Initially, average total cost falls significantly from 2.4 to 1.33.

That can be explained by the fact that average fixed cost falls so significantly in the beginning. while average variable only falls a little bit. As we go from 105 to 145 units, average fixed cost still falls, but average variable cost starts to rise, but by only a small amount, and so average total still continues to fall.

As we go from 145 to 175 units, average fixed still falls, but it's not falling as fast. It's starting to slow down. It's starting to taper off as we produce more output. But average variable is starting to rise by a little bit more. But we're still seeing that decrease in our average total from 1.1 to 1.03.

Finally, as we go from 175 to 180 units, average fixed cost only falls by a penny. But now average variable cost increases by 10 cents. And so the net result... is we start to see a rise in our average total cost.

So average total cost will always initially fall and then start to rise again. What about the last cost, marginal cost? The additional cost that we incur to produce just one more unit. As we go from 0 to 50 units, we incur 0.4 cents or 40 cents in additional cost.

When we go from 50 to 105, marginal cost continues to fall. But when we get to 145 units, marginal cost starts to rise. This follows the same pattern that we saw for our average variable cost. An initial dip and then an ultimate rise.

Well, remember where our costs are coming from, in particular from variable costs. They're coming from our wages. And in marginal cost, we're asking the question, how much more cost do we incur to make one more unit?

But the key concept here is what are our inputs doing? In other words, what's the marginal product of production and how much are we getting out of it? When we consider how that relates to cost, these relationships are clearly explained. As we hire more and more workers, at least initially, one worker to two worker in Sam's factory was more productive, and therefore his average variable cost and average mark. and marginal cost fell.

But as he hired that third worker, remember we reached diminishing marginal returns, meaning that we weren't getting as much output even though we were paying the same costs. Therefore, spreading that across all the units, costs start to rise from 0.38 to 0.41 for average variable or from 0.36 to 0.5 for marginal costs. In other words, these costs ultimately rise because of the concept of diminishing marginal product.

Diminishing marginal product is going to be the driver for a lot of these cost concepts. In other words, it's going to be the driver that ultimately forces up the cost of production for any firm. If we graph these individual cost curves for SAM, what we see is some of those relationships in action.

As you can see here, remember your average fixed cost is always falling and you can see that in the orange line in the graph. The green line reflects your average variable cost. As we begin to see more and more cost incur, we're going to see more and more average variable cost.

And you can see it's relatively flat, but it does start to rise. Your yellow is going to reflect your average total cost. So your average total cost reflects the sum of both your average fixed in orange and your average variable in blue. Finally, or I'm sorry, average variable in green. The blue reflects your marginal cost, the ultimate rise in cost, and substantial one at that.

There's some key relationships and key traits of these graphs that we can include. First, we said that average fixed cost is always falling. It's always falling because you're taking a number that never changes in the numerator of your ratio and always increasing the bottom.

Average fixed costs, therefore, will always be decreasing for any type of production. But it is important to note that the value will never become zero. It may get very, very small, but it will never become zero. Second, marginal cost is always going to intersect at the minimum of the average total cost curve.

This is conceptually what's known as the minimum efficient scale, or sometimes just called the efficient scale. The marginal cost also intersects the minimum of your average variable cost, but that's less important for us right now. The key idea is that because average total cost initially decreases, but then starts to increase again, we're going to see that same relationship for marginal cost as well.

Marginal cost will initially fall, then rise, and all of these are being driven by this idea of diminishing marginal product. So we could generalize our cost curves with these key traits, and we could see that your typical set of cost curves is going to look something like this. Average fixed cost is always falling, and so that's very easy to identify. Your average fixed cost is here. We know that our average variable cost is an additional cost that's incurred, but it's going to initially dip and then rise again.

But it can never be as... as much as average total because average fixed and average variable have to sum to meet average total. So my average variable cost will be here and average total cost here. Finally we know from our traits that your marginal cost will always intersect the average variable cost at its minimum and the average total cost at its minimum. And so this graph reflects marginal cost.

These typical sets of cost curves will help us to analyze and understand the profit maximizing decision for the different types of firms that we face. Remember, as said before, all firms face the same sorts of costs. All firms have to hire workers. All firms have to buy materials. All firms face time constraints.

So all firms are going to face these challenges and all firms are going to face the issue of diminishing marginal product, the ultimate driver of rising costs.

Transcript for:Understanding Cost Analysis in Production

Transcript for:
Understanding Cost Analysis in Production