# Elasticity of Supply

Instructor: Alex Tabarrok, George Mason University

When is a supply curve considered elastic? What are determinants of elasticity of supply? Let's compare Picasso paintings and toothpicks. Which has an elastic or

When is a supply curve considered elastic? What are determinants of elasticity of supply? Let's compare Picasso paintings and toothpicks. Which has an elastic or inelastic supply? For which good could you increase production at a low cost? We also go over how to calculate the elasticity of supply, including using the midpoint formula.

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## Transcript

In our last two videos, we covered the elasticity of demand. We now turn to the elasticity of supply.

The elasticity of supply measures how responsive the quantity supplied is to a change in the price. So it's almost the same as the elasticity of demand except instead of measuring the responsiveness of the quantity demanded, it measures the responsiveness of the quantity supplied to a change in price. A supply curve is said to be elastic when an increase in price increases the quantity supplied by a lot. And similarly vice versa, that is when a decrease in price decreases the quantity supplied by a lot then we say that the supply curve is elastic. So when the quantity supplied is very responsive to the price, we say the supply curve is elastic. When the same increase in price increases the quantity supplied by just a little then the supply curve is said to be inelastic. So when the quantity supplied doesn't vary very much with the price, the supply curve is inelastic.

Here, we show this on a graph, so consider the first curve. A \$10 increase in price on this curve -- here's the \$10 increase in price -- increases the quantity supplied from 80 to 85 units, that is not by very much. On the other hand, on this more elastic supply curve, the same \$10 increase in price increases the quantity supplied now from 80 units to 170 units. So you get a much bigger change in the quantity supplied from the same price increase when the supply curve is elastic compared to when it is inelastic. And again as with demand curves, elasticity is not the same thing as slope. Nevertheless, when you have two curves which go through a common point then the one which is flatter is more elastic at any given quantity. The one which is steeper is more inelastic. So we can always look at two curves and say this curve is more elastic than the steeper curve. And that will work for everything we're going to do in this class.

So what are the major determinants of the elasticity of supply? First and most importantly, how do unit costs change with increased production? Second, the time horizon. Third, share of market for the inputs. And fourth, geographic scope. I'll explain each of these in turn.

The main determinant of the elasticity of supply is how quickly per-unit costs increase with an increase in production. In particular, if increased production requires higher costs, then the supply curve will be inelastic. It will be steep if we're comparing two curves. On the other hand, if production can increase with constant cost or without increasing per unit cost very much, then the supply curve will be elastic.

Let me give you two examples to make this clear. Compare the following two goods -- Picasso paintings and toothpicks. Which has an inelastic supply and which an elastic supply? Okay, so let's think about an increase in price. For which good is it easier to expand production? For which good can you increase production at low cost without pushing costs up? Clearly, toothpicks. So an increase in the price of toothpicks -- and you can make lots more toothpicks just by running an additional log down the sawmill. Many, many more toothpicks without an increase in cost. On the other hand, it's basically impossible to get an increase in the production of Picasso paintings. He simply isn't producing anymore. We may still have an increase in the market supply of Picasso paintings. Some people who have them in their homes will put them onto the market. But basically the supply of Picasso paintings is highly inelastic. The price can go up and up and up and up and you're not going to get very many more Picasso paintings. Once again on the other hand, if the price of toothpicks goes up even a little bit, you're going to get a lot more toothpicks. So the supply of toothpicks is elastic and the supply of Picasso paintings is inelastic.

The time horizon influences the elasticity of supply for a good. and this is really just a logical consequence of the fact that elasticity depends upon cost and how easy it is to expand production. Immediately following a price increase, producers can expand production or output only by using their current capacity, so that tends to make supply more inelastic.

So for example, if we're talking about grain production. If the price of grain goes up, well farmers can get a little bit more grain out of their field by threshing, by going over the fields more carefully, but they're not going to get a lot more until a year or two down the line, until after they've had a chance to plant more acres of grain. On the other hand as I just said, over time producers can expand their capacity. So in the short run, the elasticity of supply tends to be more inelastic because it's harder to expand output at the same cost. Over time, however, because producers can expand their capacity, the supply curve tends to be more elastic. So supply curve tend to be more elastic, the more time you give producers to respond to the price.

The elasticity of supply also depends on whether the good in question is a small or big demander in its input markets. That is the industry's share of the demand for its inputs. Let me explain. Supply will tend to be more elastic when the industry is a small demander in its input markets. Because then supply can be expanded without causing a big increase in the demand for the industry's inputs.

Let's go back to the toothpick example. One of the reasons why toothpicks have an elastic supply is because we can easily double the supply of toothpicks and have just a tiny impact on the demand for wood on the input into toothpicks. So we can double the supply of toothpicks and since toothpicks are just a small user of wood, we don't require much more wood so we're not going to increase the demand for wood very much when we increase the demand for toothpicks. Therefore the price of wood is not going to be pushed up when we demand more toothpicks. Therefore the quantity supplied of toothpicks can easily increase at the same price without increasing the cost of toothpicks.

On the other hand, supply will tend to be inelastic when the industry is a big demander in its input markets. So again suppose that the demand for automobiles were to increase. In order to expand the supply of automobiles we need more steel, but automobiles are a big demander of steel. So when we want to increase the supply of automobiles, we're going to use a lot more steel that's going to push up the price of steel, therefore that's going to increase the price of an input into making automobiles which is going to push the price of automobiles up. Therefore the supply of automobiles will tend to be more inelastic because when we try and increase the supply of automobiles, we're going to increase the price of steel that increases the cost of producing automobiles.

The geographic scope of the market is another determinant of the elasticity of supply. In particular, the narrower the scope of the market, the more elastic the supply. The wider the scope of the market, the less elastic the supply.

For example, suppose that the demand for gasoline increases in Washington D.C., say more people are moving to the D.C. region. Well, that demand can easily be supplied by taking a little bit of gasoline from elsewhere in the country and we can increase the supply of gasoline in Washington, D.C. very easily without pushing up the price of gasoline hardly at all. On the other hand, if the worldwide demand of gasoline went up say because China is becoming richer, India is becoming richer. They're buying more automobiles. Well in that case, we're going to have to dig for more oil. We're going to have to search for more oil. That's going to be much more expensive to increase the supply of gasoline to the world than it is to increase the supply of gasoline to Washington, D.C. Again, both of these are simply a reflection of the fundamental idea -- Does an increase in the supply of a good, does that require a big increase in the cost of producing the good? So it's very easy to increase supply in Washington, D.C. or in a particular state and so forth. It's much more difficult to increase the total supply.

Okay. Let's summarize. What makes a supply curve more elastic? Fundamentally, a supply curve will be elastic when it's easy to increase production at constant unit cost or when it's easy to increase production without increasing the unit cost very much. Supply curves tend to be more elastic in the long run compared to the short run. They tend to be more elastic when the good has a small share of the market for its inputs, so it doesn't raise the price of its inputs when the market expands. And goods tend to be more elastic when we're just talking about the local supply of a good rather than the global supply which tends to be less elastic. The elasticity of supply is defined as the percentage change in the quantity supplied divided by the percentage change in the price. So, that's exactly the same as for the elasticity of demand with the exception being that instead of talking about the quantity demanded, we're talking about the quantity supplied. In mathematical notation, the elasticity supply is the percentage, delta for change in, percent of change in the quantity supplied divided by the percent of change in the price.

Here's an example. If the price of cocoa rises by 10% and the quantity supplied increases by 3%, then the elasticity of supply for cocoa is: So, elasticity percentage change in quantity supplied, that's 3%, divided by the percentage change in the price, 10%. So the elasticity must be 0.3. Here's our midpoint formula. Again practically the same as that for the elasticity of demand, only we're dealing with the quantity supplied rather than the quantity demanded. So the percentage change in quantity supplied is the change in quantity supplied divided by the average quantity times 100. The percentage change in price is the change in price divided by the average price times 100. The hundreds cancel out so we're left with this formula where the change in quantity is quantity after minus quantity before over the average quantity. Price after minus price before over the average price.

Let's do an example. At the initial price of \$10, the quantity supplied is 100. When the price rises to \$20, the quantity supplied is 110. So let's remember our formula -- change in quantity over average quantity, change in price over average price. So the quantity after is 110, the quantity before is 100, so the change in quantity is 110 minus 100. This is the average quantity. The change in price is 20 minus 10. Just make sure that since we started here with the quantity after being 110, that's associated with the price after of 20 so put the 20 first. 20 minus 10 is 10 over the average price, etc., etc., etc. You can calculate the numbers and what you find is the elasticity is .143. As with the elasticity of demand, if the elasticity of supply is less than one, the supply curve is said to inelastic. If it's greater than one, the supply curve is said to be elastic. If it's equal to one, it's said to be unit elastic.

Okay, that's it for the mechanics of the elasticity of supply. What we're going to do next is applications of the elasticity of supply. This is an extremely important part of the course so make sure you do follow the applications, learning how to apply these ideas in the real world, showing what the real world consequences of these different elasticities are is extremely important. That's what we're going to do next and that will bring us back to that question we asked at the very beginning -- How can we analyze something like the redemption of slaves, whether this is going to be a good policy or a bad policy? The elasticity of supply turns out to be critical to understanding that question, that's what we're going to look at next. Thanks.

Good question. The supply and demand curve are theoretical constructs or tools for thinking. When we say that at a higher price the quantity demanded would be less or the quantity supplied would be more, we are talking about a counter-factual state of affairs in which all else is equal except for the change in the price. Thus, when we say the long-run supply curve is more elastic than the short run supply curve we are saying that people will respond more given greater time but again we are holding all else constant.

When we want to estimate demand and supply curves then you are absolutely right we rarely have all-else-equal experiments and so other things change as time changes. As a result, when estimating supply and demand curves we need to bring to bear the tools of econometrics and statistics to control for other factors and to focus in on the data in a way which handles causality. We hope to cover econometrics in another course but fortunately there is plenty to learn from theory before we get to estimation.

In the real world, as opposed to theoretical constructs, there are many factors that affect the final results. So far, the lessons are based on an all else being equal basis. The only things being changed are demand and supply as affected by price.

In the example of taxes, higher taxes means that the employee takes less money home at the same compensation level.

Given that various sorts of compensation have different tax rates, they may prefer that a raise be in terms of a better health insurance plan, which is not taxed, than in take home pay, which is. Or they may prefer stock options that can be exercised at whatever point in the future does them the most good financially, but profits from exercising those options isn't taxed at the time.

For some people, part of their compensation isn't based directly on time worked or when that work takes place. So if a tax increase is announced in July for the following year and the normal time that bonuses are given out is in January, those bonuses might be distributed in December instead, when they would be taxed at the current lower rates.

In order to get a higher take home pay, a person may have to work more and decide that, given the higher tax rate, it's just not worth the extra hassle.

Those are just a few ways that people respond to a change in tax rates. Given the complexity of the tax code and the various values individuals place on different types of income, there are thousands of combinations of changes any particular person may choose. It's impossible to predict exactly what the net changes in the real world will be because everything is always changing. At best, numerical economics is useful for generalizations, for understanding the directions and magnitudes that various changes will most likely change outcomes.

Real world curves are never straight lines. They aren't even smooth curves. People aren't machines and no one can have all the knowledge available to know exactly what the final outcome will be, especially when you look at longer time frames where the market (at least a free market), both buyers and sellers, are always trying to come up with new substitutes and more efficient ways to use any given good. In general, the less elastic a curve, the more effort is put into making it more elastic so it can better respond to changes in the market of any kind. That's just as true for taxes as any more tangible item.

For second last question, I think it can be explained with time horizon. As the tax incresea, in short run, people's income will decrease. In long run, people will find way to reduce their taxed amount, such as cash out part of it. Eventually, the taxed income for the government will be less higher than when the policy was initiated.

For the last one , basically just use the formula: Elasticity=ΔQ/ΔP
In short run: 1.4= ΔQ/10;
In long run:0.1=ΔQ/10

For first year, individual can respond to the coming increased tax on earnings by taking some earnings early (that is, in the previous year; see above regarding executive power to take payments early). Thus a higher tax (decreased net income) can produce a greatly reduced taxable income. After the first year, many of these tax-avoidance strategies will not be available any more (since taxes for every year are now higher). So, taxable income will remain nearly the same for subsequent years (unless there's another really big tax rate hike). Thus an elastic supply curve for first year becomes inelastic over long term. But I understand your confustion (see my own question below, but I think this is the answer).