15 General Equilibrium

15.1 General Equilibrium Effects in Action

General equilibrium analysis has two parts. One part describes the mechanics of market interactions and illustrates how various market features affect the size and direction of equilibrium effects in all these markets. This branch of general equilibrium analysis describes markets as they are. The other part asks whether economy-wide market equilibria are efficient or equitable (and explains how to define those terms). You could say this type of analysis focuses on markets as they ought to be. People will never fully agree on how markets ought to behave, but general equilibrium analysis at least gives us a way to describe how it can work.

These two approaches use somewhat different frameworks for thinking about general equilibrium, and are in some respects independent of each other. Later in the chapter, we look at how the second approach works. In this section, we discuss the first approach and learn how general equilibrium effects work in markets and what market features influence these mechanisms.

An Overview of General Equilibrium Effects

The Energy Policy Act of 2005 set mandates to encourage the use of renewable fuels, including biofuels like ethanol, in the United States. It required that billions of gallons be used in the years that followed, and they were amounts well above the quantities a freely operating market would provide. For various technological and cost reasons, virtually the entire mandate was met with the use of corn-based ethanol. From an economic perspective, then, the Act increased the demand for corn and shifted the demand curve for corn outward.

naran/iStock/Thinkstock
iStockphoto/Thinkstock

Can the use of corn to make biofuel lead to an increase in the price of wheat?

Recall that in the Chapter 8 Application “The Increased Demand for Corn”, we analyzed how this might affect the equilibrium price and quantity in the corn market. The increase in demand should drive up prices and induce more production: Corn producers would plant more, and wheat, soybean, or rice farmers would switch some of their production to corn. The increase in demand moves the market up its supply curve (because marginal costs rise with the added production), and raises the equilibrium price and quantity of corn. These predictions of the theory were borne out following the passage of the Act: Corn production grew 11% between 2005 and 2011, and prices more than doubled.1

Yet, corn wasn’t the only commodity crop that saw large price increases during this same period. Wheat and rice prices grew by two-thirds, and soybean prices doubled. General equilibrium suggests that the price increases in these markets might be related, even though the other crops had no direct role in meeting the renewable fuels mandate. An increase in the price of corn increases the demand for corn substitutes (such as wheat, rice, and soybeans).

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These cross-market effects don’t stop there. Higher corn demand also increases the demand for the inputs farmers use to produce it. Those inputs may have upward-sloping supply curves of their own, so the increased demand for corn may also drive up the prices of farm machinery, fertilizer, or farmland. That’s what happened in real life, too: Between 2005 and 2011, the prices of agricultural chemicals and the average value of an acre of cropland rose by about 50%.2 Furthermore, the increased demand for substitutes like wheat also helped drive up the cost of the inputs used to make the substitutes.

All these spillover effects on other markets bounce back and affect the corn market itself. Figure 15.1 demonstrates how this feedback might work. Panel a shows the corn market. Before the renewable fuels mandate, the market is in equilibrium with demand curve D_c₁ and supply curve S_c₁, and the equilibrium quantity and price are Q_c₁ and P_c₁. The direct effect of the mandate is to increase the demand for corn from D_c₁ to D_c₂. In a partial equilibrium analysis, we’d expect this to increase the quantity and price of corn to Q_c₂ and P_c₂, respectively, and we’d be done.

Figure 15.1: Figure 15.1 General Equilibrium Effects in Corn and Wheat Markets

Figure 15.1: (a) Before the renewable fuels mandate, the corn market is in equilibrium at (Q_c₁, P_c₁), where the initial demand curve D_c₁ and supply curve S_c₁ intersect. The direct effect of the renewable fuels mandate shifts demand out to D_c₂. Because the mandate also increases the price of wheat, however, the demand for corn continues to shift out until general equilibrium is reached at (Q_cF, P_cF), where D_cF intersects S_c₁.

Figure 15.1: (b) Wheat, a substitute good for corn, is at an initial equilibrium of (Q_w₁, P_w₁), where the initial demand curve D_w1 and supply curve S_w₁ intersect. When the renewable fuels mandate increases corn prices, the demand for wheat increases to D_w₂. The subsequent increases in corn prices continue to shift out the demand for wheat until general equilibrium is reached at (Q_wF, P_wF), where D_wF intersects S_w₁.

A general equilibrium analysis, however, recognizes that because wheat and corn are substitutes, an increase in the demand for corn will affect the wheat market as shown in panel b. Before the mandate, wheat supply and demand are at S_w₁ and D_w₁. The higher corn price caused by the renewable fuels mandate causes people to shift, say, from corn-based breakfast cereals to wheat-based cereals, thus increasing the demand for wheat from D_w₁ to D_w₂, and raising wheat quantities and prices to Q_w₂ and P_w₂.

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Now, because wheat is a substitute for corn, higher wheat prices cause the demand for corn to increase, and there is a secondary outward shift in corn demand, from D_c₂ to D_c₃. This raises the quantity and price of corn to Q_c₃ and P_c₃. Higher corn prices, in turn, shift out wheat demand again, from D_w₂ to D_w₃, raising wheat quantity and price to Q_w₃ and P_w₃, and so on.

This feedback eventually slows down and stops. The size of the secondary feedback effect is smaller than the initial demand shift from D_c₁ to D_c₂, the third shift is smaller than the second, and so on until the markets settle at a stable point. In the corn and wheat markets in Figure 15.1, the final demand curves after all the feedback effects are shown by D_cF for corn and D_wF for wheat.

Therefore, the general equilibrium effect of the renewable fuels mandate in the corn market is to increase quantity from Q_c₁ to Q_cF and price from P_c₁ to P_cF. These changes are considerably larger than the quantity and price increases to Q_c₂ and P_c₂ that a partial equilibrium analysis implies. When the links between two markets are strong, as they are between corn and wheat, the gap between the partial and general equilibrium outcomes in the corn market is larger. Moreover, in a partial equilibrium analysis, the effect of the fuels mandate on wheat quantities and prices, which increase from Q_w₁ and P_w₁ to Q_wF and P_wF, is completely ignored.

We can also analyze the supply-side/input links between industries, such as the spillovers created when two markets use common inputs. (We examine this case in detail in a later quantitative section.) In this case, higher corn demand causes the supply of wheat to fall because farmers shift some of their production from wheat to corn. This decrease in supply shifts the supply of wheat inward, and with no change in wheat demand (we ignore demand spillovers like those we just discussed to focus on supply-side links), the equilibrium quantity of wheat falls and its price rises. This is demonstrated in Figure 15.2.

Figure 15.2: Figure 15.2 Supply-Side Input Links across Industries

Figure 15.2: (a) The increase in the demand for corn shifts demand from D_c₁ to D_c₂. As a result, the quantity of corn increases from Q_c₁ to Q_c₂, and the price of corn increases from P_c₁ to P_c₂.

Figure 15.2: (b) The increased demand for corn causes farmers to shift some of their production from wheat to corn. Consequently, the supply of wheat shifts in from S_w₁ to S_w₂. The quantity of wheat decreases from Q_w₁ to Q_w₂, and the price of wheat increases from P_w₁ to P_w₂. The resulting increase in the wheat price feeds back in turn to the corn market, shifting the supply of corn from S_c₁ to S_c₂, reducing the quantity of corn to Q_c₃ and raising its price to P_c₃, because of increases in the price of inputs into corn production.

The decrease in wheat supply from S_w₁ to S_w₂ and the resulting increase in its price feed back, in turn, to the corn market and shift the supply of corn from S_c₁ to S_c₂ because this raises the price of inputs into corn production.

Now that we have an overview of how general equilibrium works, the next two subsections put actual numbers to the two cases we’ve just discussed to make the process of determining general equilibrium effects more explicit.

Quantitative General Equilibrium: The Corn Example with Demand-Side Market Links

Let’s put some specific numbers on the types of processes discussed above to get a better feel for analyzing general equilibrium effects. To simplify our analysis, we assume that wheat and corn are the only two goods in the world. In this world, general equilibrium is the set of wheat and corn prices that simultaneously equate supply and demand in both markets.

We consider two numerical examples. In this section, we look at the cross-market general equilibrium effects that arise because of demand-side links between the wheat and corn markets (i.e., because consumers’ preferences for wheat and corn are interrelated). In the next section, we look at how supply-side links between the markets (the production of wheat and corn is interrelated) drive the general equilibrium effects.

Let’s suppose the supply of wheat is , where is the quantity of wheat supplied (in millions of bushels) and P_w is the price of wheat (in dollars per bushel). This supply curve has the typical upward slope: The quantity of wheat supplied increases as wheat prices rise. Similarly, corn supply is , where is the quantity of corn supplied (in millions of bushels) and P_c is the price of corn (in dollars per bushel). This supply curve also slopes upward; the quantity of corn supplied increases as corn prices rise.

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Now let’s say wheat demand is given by the equation . This equation tells us that, as with a standard demand curve, the quantity of wheat demanded decreases as wheat prices rise. But notice that the quantity of wheat demanded is also affected by corn prices P_c: When they increase, so does . This second effect reflects the fact that wheat is a substitute for corn. Therefore, higher corn prices cause consumers to shift some corn purchases toward wheat. This raises the quantity of wheat demanded at any given wheat price and shifts out the wheat demand curve. We assume corn demand is given by the equation . Thus, corn is a substitute for wheat; higher wheat prices shift out the demand for corn.

The fact that wheat and corn are substitutes for each other in this example is what creates general equilibrium effects. If we had assumed that wheat demand and corn demand were only a function of their own prices (while keeping the same supply curves that we assumed above), no cross-market effects would occur. Changes in wheat prices wouldn’t shift the demand for corn, and vice versa. As a result, there would be no general equilibrium impact of one market’s price on the other.

Finding Equilibrium Prices Describing the general equilibrium in this two-good economy requires figuring out what prices equate supply and demand in both markets. We start with the wheat market. Substituting the supply and demand curves above into the partial equilibrium condition that the quantity of wheat supplied must equal the quantity demanded, we have

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P_w = 20 – P_w + P_c

We can rearrange this equation to express the equilibrium wheat price in terms of the price of corn:

Repeating the same steps for corn (equating the quantity supplied and demanded and solving for the corn price in terms of the wheat price) gives

These equations look similar to each other because we set up the example so that the two markets have identically shaped supply and demand curves.

The two equations for wheat and corn prices make clear that each market’s equilibrium price depends on the other’s. This is the essence of general equilibrium. We can find the prices that put both markets in equilibrium by substituting for P_c in and solving for P_w:

P_w = $20

The general equilibrium price for wheat, then, is $20 per bushel.

To find corn prices in general equilibrium, we substitute the wheat price P_w = 20 into the equation for the price of corn:

Corn prices are also $20 per bushel. That corn and wheat prices are the same is a special case, once again, because we assumed the two markets have identically shaped supply and demand curves.

Finding Equilibrium Quantities Given the equilibrium prices of $20 per bushel, we can calculate the general equilibrium quantities of wheat and corn by substituting P_w = 20 and P_c = 20 into the supply or demand curve equations for wheat and corn:

	For wheat	For corn
Supply

Demand


Equilibrium Q

The general equilibrium quantities for wheat and corn are therefore both 20 million bushels.

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This is the initial general equilibrium in the economy (akin to quantities and prices Q_c₁, Q_w₁, P_c₁, and P_w₁ in our example in the previous section).

General Equilibrium Effects Now let’s look at how an isolated change in one market can create general equilibrium effects in the other. Suppose the renewable fuels mandate increases the demand for corn by 12 million bushels at any given set of corn and wheat prices. As a result, the demand curve for corn becomes

This is reflected in the shift of corn demand from D_c₁ to D_cF in Figure 15.3.

Figure 15.3: Figure 15.3 The Effects of a Renewable Fuels Mandate on the Markets for Corn and Wheat

Figure 15.3: (a) Before the renewable fuels mandate, the corn market supplies 20 million bushels of corn at a price of $20 per bushel, where D_c₁ intersects S_c₁. When the demand for corn shifts out to D_c_F, corn’s price increases to $28 per bushel, and its quantity increases to 28 million bushels.

Figure 15.3: (b) Wheat, a substitute good for corn, is at an initial equilibrium of 20 million bushels at $20 per bushel, where initial demand curve D_w₁ and supply curve S_w₁ intersect. When the renewable fuels mandate increases corn prices, the demand for wheat increases to D_wF. The wheat market now supplies 24 million bushels of wheat at a price of $24 per bushel, where D_W₂ intersects S_w₁.

We know that prices have to change—if they stayed at $20, the quantity of corn demanded would be 32 million bushels but the quantity supplied only 20 million bushels. To find out what the new general equilibrium price is in the corn market, we have to repeat our steps above using the new corn demand curve.

Because the supply and demand curves for wheat are not directly changed by the mandate, the equation for the price of wheat in terms of corn remains the same ( ). But, the equation for the equilibrium price of corn, which was , changes because of the new corn demand curve. Setting , we now have

P_c = 32 – P_c + P_w

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Again, we can solve for the general equilibrium wheat price by plugging one price equation into the other. This gives

P_w = $24

The price of wheat is now $24 per bushel. Substituting this price back into the new price of corn equation shows that the new equilibrium corn price is per bushel. We then plug these prices into the supply or demand curves to obtain the new general equilibrium quantities:

Summing Up We’ve just seen how an increase in the demand for corn leads not only to higher corn prices and quantities, as we would expect from a partial equilibrium analysis that just looks at what happens in the corn market, but also to higher wheat prices and quantities. Not surprisingly, the price increase is greater for corn (an $8 per bushel, or 40% increase) than for wheat (a $4 per bushel, or 20% increase). Notice how wheat prices rose even though the initial change in the economy—the increase in corn demand—did not directly affect the wheat supply and demand curves. The general equilibrium effect works instead through prices of substitute goods and was not included in our previous analyses of markets.

figure it out 15.1

For interactive, step-by-step help in solving the following problem, visit LaunchPad at http://www.macmillanhighered.com/launchpad/gls2e.

Whiskey and rye are substitutes. Suppose that the demand for whiskey is given by Q_w = 20 – P_w + 0.5P_r, and that the demand for rye is given by Q_r = 20 – P_r + 0.5P_w, where Q_w and Q_r are measured in millions of barrels and P_w and P_r are the prices per barrel. The supplies of whiskey and rye are given by Q_w = P_w and Q_r = P_r, respectively.

Solve for the general equilibrium prices and quantities of whiskey and rye.
Suppose that the demand for whiskey falls by 5 units at every price so that Q_w = 15 – P_w + 0.5P_r. Calculate the new general equilibrium prices and quantities of whiskey and rye.

Solution:

We first need to solve for the price of whiskey as a function of rye by setting quantity demanded and quantity supplied equal in the whiskey market:

20 – P_w + 0.5P_r = P_w

2P_w = 20 + 0.5P_r

P_w = 10 + 0.25P_r

Then, we follow the same step for the rye market so that we have the price of rye expressed as a function of the price of whiskey:

20 – P_r + 0.5P_w = P_r

2P_r = 20 + 0.5P_w

P_r = 10 + 0.25P_w

To solve for P_w, we can substitute in the equation we just derived for P_r:

P_w = 10 + 0.25P_r = 10 + 0.25[10 + 0.25P_w] = 10 + 2.5 + 0.0625P_w

0.9375P_w = 12.5

P_w = $13.33

This means that P_r is

P_r = 10 + 0.25P_w = 10 + 0.25(13.33) = 10 + 3.33 = $13.33

Because Q_w = P_w and Q_r = P_r, Q_w = 13.33 million barrels and Q_r = 13.33 million barrels.
When the demand for whiskey falls, both the markets for whiskey and rye will be affected. We will need to follow the same steps used in part (a) to solve for the new equilibrium prices and quantities.

First, we solve for the price of whiskey as a function of the price of rye:

15 – P_w + 0.5P_r = P_w

2P_w = 15 + 0.5P_r

P_w = 7.5 + 0.25P_r

Because the supply and demand for rye are not affected initially, we know from part (a) that

P_r = 10 + 0.25P_w

Therefore, we can substitute P_r into the equation for P_w:

P_w = 7.5 + 0.25P_r = 7.5 + 0.25[10 + 0.25P_w] = 7.5 + 2.5 + 0.0625P_w

0.9375P_w = 10

P_w = 10.67

Substituting for P_w and solving for P_r, we get

P_r = 10 + 0.25P_w = 10 + 0.25(10.67) = 10 + 2.67 = 12.67

Because Q_w = P_w and Q_r = P_r, Q_w = 10.67 million barrels and Q_r = 12.67 million barrels.

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Application: The General Equilibrium of Carmageddon

In July 2011 residents of metropolitan Los Angeles prepared for disaster. Residents stocked up on food so they wouldn’t have to leave their houses for the weekend. Hospitals put into effect emergency procedures to ensure they would have enough staff. Local news stations planned for live coverage.

The city wasn’t preparing for a massive flood or military attack. Instead, they were getting ready for “Carmageddon,” a weekend-long construction project during which the 405, one of the main freeways connecting Los Angeles to outlying areas, would be closed.

The city government hoped that when the project was finished, it would lessen congestion and commute times on the notoriously busy Los Angeles freeways. To this end, officials planned to build an additional lane and add a carpool lane to encourage people to share their commutes with coworkers. How successful were these measures? Was Carmageddon worth all of the hassle?

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3Gilles Duranton and Matthew A. Turner, “The Fundamental Law of Road Congestion: Evidence from US Cities,” American Economic Review 101, no. 6 (October 2011): 2616–2652.

It’s too early to tell for Los Angeles—some aspects of the construction project are still under way—but a recent paper by economists Gilles Duranton and Matthew Turner suggests that the construction project is not likely to make much difference to commuters because of general equilibrium effects.3

Over the past 20 years, as the U.S. roadway system expanded, the average number of cars on the road in metropolitan areas nearly doubled. Using this fact as a jumping-off point, Duranton and Turner examined more closely the effects of increasing the number of highways and major roadways on traffic in urban areas. In particular, the researchers looked at the effect of the number of lane-kilometers in an area on vehicle-kilometers traveled. Lane-kilometers are the product of a road’s length and its number of lanes, capturing the road’s total vehicle-carrying capacity. Vehicle-kilometers are the product of the number of vehicles on the road and the average distance a vehicle travels.

What they found would probably shock the Angelenos: The elasticity between vehicle-kilometers traveled and lane-kilometers is approximately 1.03. That is, for every increase in roads’ traffic-carrying capacity, there was a one-for-one increase in how much people drove. So, for example, if the 405 expansion added 10% to the highway’s ability to handle traffic, you could expect the number of cars on that stretch of highway to grow by 10%, too. Thus, even as measures are taken to improve congestion, the traffic that commuters face seems to hold steady.4

Why doesn’t the density of cars on the road decrease as the number of roads increase? When Los Angeles builds a highway to improve traffic, the city is relying on a partial equilibrium analysis. Unfortunately, this problem involves general equilibrium effects—an increase in roadways in an area has effects beyond those predicted by partial equilibrium analysis. The Duranton and Turner study documents that expanding the supply of roadways encourages more businesses and people to move to the area and farther out from downtown. This resulting increase in drivers’ demand for roadways continues until traffic in the area converges to its “natural” steady level.

These findings indicate that Los Angeles gridlock is unlikely to be improved by highway expansion. But, there was one unexpected benefit of Carmageddon on area traffic: Because most people stayed home that weekend, those who did take to the roads faced practically empty roadways for a couple of days.

Quantitative General Equilibrium: The Corn Example with Supply-Side Market Links

In the example just covered, the link between the corn and wheat markets was on the demand side. The two products were substitutes, so the change in one good’s price affected the demand for the other. Supply-side links can create general equilibrium effects as well. Corn production and wheat production, for example, use common inputs (fertilizer, land, farmers).

Again, let’s start with some specific and simple forms for the supply and demand curves. Suppose the demand curve for wheat is and the demand curve for corn is . Notice that the demand-side links between the markets are now gone. Only a good’s own price affects its quantity demanded. We are looking at a situation in which there is no demand-side interaction between markets, only supply-side interactions.

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The supply curves are now for wheat and for corn. You can see the connections between the two markets in these new supply curve equations. The quantity supplied of each good increases as its own price increases and decreases as the other good’s price increases. This relationship captures the notion that when one good’s price increases, production shifts toward that good, allocating scarce resources away from production of the other good (such as replanting wheat fields as corn fields).

We can solve for the general equilibrium prices and quantities using the same steps we followed in the demand-side market links analysis. (Here, we skip some of the details because we’ve already done these types of calculations.) Setting and solving for the price of wheat in terms of the corn price give

Again, the symmetry of how we’ve set up these markets will result in a similar solution for corn prices: . If we solve this system of equations, we find that P_w = $10 per bushel and P_c = $10 per bushel. If we substitute these prices into the supply and demand curves, we find that the quantities of both wheat and corn in this general equilibrium are 10 million bushels.

Now again suppose there is a 12 million bushel increase in the quantity demanded of corn at all prices because of the renewable fuels mandate, so that . The equation expressing the wheat price as a function of the corn price is the same as above because the supply and demand curves for wheat are not directly affected. The equation for the price of corn changes, though. It’s now When we solve this equation and the one for wheat prices above, we find that P_w = $11.50 and P_c = $14.50 per bushel. Plugging these prices into the supply or demand curves shows that the equilibrium wheat quantity is 8.5 million bushels and the equilibrium quantity of corn is 17.5 million bushels.

Summing Up As in our previous example, an increase in corn demand leads to increases in both corn and wheat prices in general equilibrium. This is true in markets like this one where there are supply-side interactions between markets, just as it was in the market with demand-side links.

With supply-side links, higher corn prices move production from wheat to corn, thus decreasing the quantity of wheat supplied at every price, and shifting in wheat’s supply curve. Because the demand curve for wheat does not change, wheat prices rise. Also, just as in the case of demand-side links, the price increase is larger for the good receiving the direct demand shift (corn).

However, notice that these similarities do not necessarily mean that demand-side market links create the same general equilibrium effects as supply-side connections. While the prices of all goods go up in both cases, their implications for quantities differ. In the demand-side link case above, the general equilibrium quantities of both goods increased in response to the demand shift for corn. In the supply-side case we just discussed, though, while equilibrium corn quantities rose, wheat quantities fell.

The quantity results are different because with the demand-side connection between the two markets, the increase in the demand for corn also increased the demand for wheat. Because the supply curves in both markets were fixed, these increases in demand led to increases in both quantities. With supply-side connections, however, the increased demand for corn resulted in a decrease in the supply of wheat, lowering its equilibrium quantity. These opposing predictions about the quantity changes in the wheat market give us a way to test whether the general equilibrium corn and wheat price increases are caused by demand-side or supply-side across-market effects. If the two goods are substitutes, then demand-side linkages imply that wheat quantities rise in response to the increased corn demand. If wheat quantities fall, on the other hand, this suggests supply-side links are more important.5

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FREAKONOMICS

Horse Meat and General Equilibrium

If you’ve ever shopped at IKEA, chances are that after picking out a ready-to-assemble bed frame or a fish-shaped ice cube tray, you probably headed to their in-store bistro for a bite to eat. Their signature Swedish meatball meal includes 15 meatballs, along with mashed potatoes, cream sauce, and lingonberries, for under $5. At that price, there are sometimes long lines.

But not in February 2013.

That’s when it was revealed that Ikea’s meatballs (supposedly all-beef) actually were partly made of horsemeat.

These meatballs are delicious and cheap, too. I wonder what seasonings have been added?

IKEA was just one of a long list of European companies caught up in a massive horsemeat scandal. Consumers reacted sharply to the scandal—demand for the affected products plummeted in the following weeks. Frozen burgers, for instance, saw a decrease in sales of 41% in March and April 2013. But the scandal’s impact ranged far beyond the market for processed beef.

When consumers reduced their consumption of processed meats, they didn’t just eat less. Instead, they found substitutes. In February 2013 the National Federation of Meat and Food Traders reported a 30% increase in sales of beef burgers at independent butchers. Wary of purchasing processed products from the large supermarkets, consumers instead opted for meat from more trustworthy sources. As Brindon Addy, owner of a Yorkshire shop and chairman of an organization of local butchers, said, “Health scares are always good for us.”

Vegetarian products also experienced a boost following the horsemeat scandal. In a survey by research firm Consumer Intelligence, 6% of respondents said they knew someone who went vegetarian as a result of the scandal. And this response was reflected in the market—in the second half of February, Quorn, a heavyweight in the U.K. vegetarian ready-meal market, saw sales growth more than double.

General equilibrium sometimes seems abstract when it’s taught in a textbook, but it is a powerful economic force. Vegetarian food producers and storefront butchers tend not to see eye to eye on most issues, but one thing they can definitely agree on: More demand for their product, even if driven by changes in another market, is better.

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Application: General Equilibrium Interaction of Cities’ Housing and Labor Markets

In these examples, we see that general equilibrium effects can show up when a price change in one market shifts supply or demand curves in other markets. But, general equilibrium effects can affect the slopes of supply and demand curves, too.

6Raven E. Saks, “Job Creation and Housing Construction: Constraints on Metropolitan Area Employment Growth,” Journal of Urban Economics 64, no. 1 (July 2008): 178–195.

Recent research by economist Raven Saks documented an example of this.6 Saks looked at how the labor markets in major cities responded to increased demand for labor by local firms. (This outward shift in labor demand is typically caused by heightened demand for the products of firms that operate in the area.) A partial equilibrium analysis of the effect of a labor demand shift in the city follows. In the short run, as firms experience increased demand for their products, their demand for labor increases and the labor demand curve shifts to the right from DL₁ to DL₂ (Figure 15.4a). Given an upward-sloping short-run labor supply curve SL_SR, this increase in demand leads to an increase in both employment and wages, as seen in the movement from equilibrium A to B.

Figure 15.4: Figure 15.4 Interaction between Labor and Housing Markets

Figure 15.4: (a) An increase in the demand for labor by local firms shifts demand from DL₁ to DL₂, resulting in a short-run increase in employment and wages from L_A to L_B and W_A to W_B, respectively. In the long run, workers from other cities migrate to the area. As a result, the long-run supply curve SL_LR is relatively elastic, and the quantity of labor supplied increases to L_C, pushing down wages to their original level at W_C = W_A.

Figure 15.4: (b) The influx of new workers has general equilibrium effects that extend beyond the labor market. As a result of the migration to the city, demand for housing DH₁ shifts out to DH₂. In a market such as Buffalo where the supply of housing (SH_Buffalo) is relatively elastic, housing prices stay constant at P₁ = P_Buffalo2. In New York City, the relatively inelastic supply of housing (SH_NYC) means that housing prices will rise to P_NYC2.

Figure 15.4: (c) New York City’s relatively steeper long-run labor supply curve (SL_LR_,NYC) reflects the increase in housing prices seen in panel b, while Buffalo’s long-run labor supply curve (SL_LR_,Buffalo) is similar to the flat supply curve in panel a. Because of the effects of the housing market on the labor market, Buffalo will experience a greater increase in employment and a smaller increase in wages than New York City.

The short-run labor supply curve slopes up because the wage must rise to induce the existing local labor force to work more. But over time, higher wages in the city will also cause workers from other cities to move in. This ability of workers to migrate across cities in response to wage changes means the long-run labor supply curve is more elastic (flatter) than the short-run labor supply curve. This long-run supply curve is labeled SL_LR in panel a. (We’ve assumed for now that the migration response is significant enough that the long-run supply curve is perfectly elastic—that’s why the curve is flat—though we’ll see in a minute this may not be true in general equilibrium.)

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The long-run migration response moves the equilibrium down the new labor demand curve from point B to point C, increasing employment further as wages fall to their original level. Once the wage equals its original level, new workers stop moving to the city, employment growth stops, and the long-run labor market equilibrium is at point C. The increase in the quantity of labor demanded from L_A to L_C is therefore the city’s long-run total employment response to the shift in the short-run labor demand curve.

Saks’ research suggested the story is more complex than this, however. General equilibrium effects arising from links between the labor and housing markets also influence the size of the long-run employment response. This is because the influx of new workers into the city due to the increase in demand in the labor market also increases demand in the local housing market. This demand shift is shown in panel b of Figure 15.4 as movement in the housing demand curve from DH₁ to DH₂. In cities with steep housing supply curves, like New York City (we discuss what determines the steepness of cities’ housing supply curves below), worker migration drives up housing prices. This increase in housing prices is seen in panel b. When the housing demand curve shifts, the market moves up along New York’s housing supply curve SH_NYC, and the price rises from P₁ to P_NYC2. In cities with more elastic supply, like Buffalo, house prices rise less or may not increase at all. In panel b, Buffalo’s housing supply curve is SH_Buffalo; there is no equilibrium price change in response to the demand shift, so P₁ = P_Buffalo2.

Any price effect in the housing market has, in turn, its own impact on the labor market. Higher housing prices counteract wage increases driven by the shift in labor demand. To spur a given amount of migration, then, wages have to rise more in cities with steeper housing supply curves, because they have to make up for the higher home prices new workers in the city face. This means that markets like New York City with steeper long-run housing supply curves have steeper long-run labor supply curves, too. Similarly, markets like Buffalo with flatter housing supply curves have flatter long-run labor supply curves. This long-run response reflects the general equilibrium connection between the local housing and labor markets. So while Buffalo’s labor supply curve looks something like SL_LR in panel a of Figure 15.4, New York City’s is steeper. Panel c of Figure 15.4 plots these two long-run labor supply curves against the initial labor demand shift. As we can see, the demand shift leads to a smaller long-run increase in total employment in more inelastic housing supply markets like New York than in more elastic housing supply markets like Buffalo.

Saks tested the hypothesis that the total employment effect of labor demand shifts in general equilibrium depends on the steepness of cities’ housing supply curves. She compared employment responses to labor demand shifts in cities with different housing supply elasticities. Although she could not measure housing supply curves directly, she showed that metropolitan areas with more legal restrictions on building (and therefore likely with steeper housing supply curves, because such restrictions make it more expensive to increase the quantity of housing supplied) had smaller long-run employment responses to equal-sized labor demand shifts. A 1% outward shift in labor demand (i.e., one that would increase local firms’ labor demand by 1% at any given wage) in cities with few building restrictions like Nashville, Tennessee, or Bloomington-Normal, Illinois, led to a long-run employment increase of about 1%. In restrictive cities like New York and San Francisco, however, a 1% increase in labor demand led to long-run employment increases that were one-third smaller.

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