Lecture 5: Specialization and Comparative Advantage

Click here for the quiz on this reading.

Last week we talked about exchange economies in which there was already an “endowment” of goods, without talking about where those goods came from. We started by analyzing how an individual would make decisions on their own; then analyzed market behavior; and finally showed how markets could help everyone in an economy do better than they could on their own.

This week we’re going to do much the same thing, but zoom out to include the production decisions that generate the initial “endowment” of goods in the exchange model. We will be examining the simplest possible production economy: one in which agents are endowed not with goods, but with time – i.e. labor – and production technologies which allow them to produce two different goods: in particular, fish (good 1) and coconuts (good 2).

Why fish and coconuts? The model we’re looking at is sometimes called a “desert island” model, with the general story roughly following the plot of Daniel Defoe’s Robinson Crusoe or, in a more modern telling, the movie “Cast Away.” In that movie, a FedEx manager named Chuck Noland is stranded on an uninhabited island somewhere in the Pacific after a plane crash. All he has are the resources on the island — stones, branches, coconut trees, fish in the water — and a few FedEx packages from the plane. With these resources, and his own time, he figures out a way to survive, mainly on the fish he catches and the coconuts he’s able to break open.

So, the first model we’ll look at is how Chuck optimally divides his time between producing fish and coconuts if he cannot trade with anyone else. Then, we’ll look at a situation in which there are two such agents, and can possibly trade with one another.

Resource Constraints and Production Possibilities

Even before Chuck is marooned on his island, he’s keenly aware of the concept of resource constraints. In the opening scene of “Cast Away,” he exhorts his crew to meet a harsh deadline for getting packages delivered to the Moscow airport:

"Time rules over us without mercy...That's why every FedEx office has a clock. Because we live or we die by the clock...Locally, it's 1:56. That means we've got three hours and four minutes before the end-of-the-day's package sort. That's how long we have — that's how much time we have — before this pulsating, accursed, relentless taskmaster tries to put us out of business."

You could be the richest person in the world, but time would still constrain your activities: even if you could afford whatever you wanted, you would only have a finite amount of time with which to enjoy it. Time is the ultimate resource constraint: an hour spent doing one thing is one hour less spent doing something else. Much of economic activity boils down to how we spend our time.

In Econ 50, we saw how time — in the form of labor input, and in conjunction with other inputs — may be transformed into a single good via a production function. Today we will examine the issue of allocating a fixed set of resources across goods, and what effect resource constraints have on what combinations of goods we can produce. After all, an hour spent producing one good is an hour less producing another.

In Chuck’s case, once he is stranded on his island, how he spends his time becomes even more important. Let’s assume Chuck can spend his time in only two ways: fishing or cracking coconuts open. Let’s call fish “good 1” and coconuts “good 2,” so we’ll call the labor devoted to fish $L_1$ and the labor devoted to coconuts $L_2$. Finally, let’s call the total amount of time Chuck has available to him (say, hours per week) $\overline L$. In this case Chuck’s resource constraint is given by the equation $L_1 + L_2 \le \overline L$ We can visualize his tradeoff of how to spend his time by plotting “labor devoted to fish” and “labor devoted to coconuts” on a graph:

See interactive graph online here.

Given his resource constraints, Chuck is going to be limited in the number of fish he can catch, and the number of coconuts he can break open. Some “bundles,” or combinations of outputs, will be possible for Chuck to produce; others will not. We will call Chuck’s “feasible set” of output bundles his production possibilities set. The boundary between that set and the set of bundles he cannot produce we’ll call his production possibilities frontier.

If Chuck is not using all of his resources – or is using them inefficiently – he will produce at a point strictly within his production possibilities set. At such a point, he can produce more fish without necessarily producing fewer coconuts, and vice versa. Along the PPF, however, he faces a tradeoff: if he wants to produce more fish, he needs to produce fewer coconuts.

Chuck’s PPF is related to his resource constraints via his production functions: depending on how he can transform labor into fish and coconuts, different combinations of output will be available to him. Note that, just like a budget set or an Edgeworth Box, the PPF exists in good 1 - good 2 space!

For today, we’re going to stick with a simple case of linear technologies: assume that Chuck has 12 hours of labor, and with each hour of labor he can catch 2 fish or collect 1 coconut. This simple setup is really saying that there is an economy with a single resource (labor) which can be used in one of two production functions: the quantity of fish, $x_1$, is given by $x_1 = f_1(L_1) = 2L_1$ and the quantity of coconuts, $x_2$, is given by $x_2 = f_2(L_2) = L_2$ For any division of labor $(L_1,L_2)$, the production functions tell us how many fish and coconuts Chuck will produce. Therefore, the set of feasible production possibilities depends on the set of feasible resource allocations.

We can illustrate this by viewing the resource constraint and the PPF side-by-side, as shown below. Drag the orange dot all the way to the right: we can see that if Chuck devotes all 12 hours of labor to producing fish, he can produce $12 \times 2 = 24$ fish. Likewise, if you move the orange dot all the way up and to the left, you can see that if Chuck devotes all 12 hours to coconuts, he can produce $12 \times 1 = 12$ coconuts.

See interactive graph online here.

How do we derive the equation of this PPF? Note that the PPF is defined by three equations:

The production functions relate $x_1$ to $L_1$ and $x_2$ to $L_2$.
The resource constraint relates $L_1$ and $L_2$ to the total supply of labor, $\overline L$.

If we invert the production functions — that is, solve each for $L$ as a function of $x$, instead of $x$ as a function of $L$ — we get the amount of labor required to produce $x_1$ and $x_2$ units of output: $\begin{aligned} L_1 &= \tfrac{1}{2}x_1\\ L_2 &= x_2 \end{aligned}$ If we plug this into the resource constraint, we get the equation of the PPF: $\begin{aligned} \tfrac{1}{2}x_1 + x_2 &= 12 \end{aligned}$ This is the equation of the red line in the right-hand panel above.

One way of thinking about this is just like a budget line: instead of money, Chuck has $\overline L = 12$ hours. Each fish “costs” half an hour to produce, and each coconut “costs” one hour to produce. Hence, we can think of this as being like a budget line where $p_1 = {1 \over 2}$, $p_2 = 1$ and $m = 12$.

Opportunity Cost and the Marginal Rate of Transformation

Anywhere along the PPF, Chuck cannot make more of both goods: if he wants to produce more fish, he needs to produce fewer coconuts, and vice versa. The slope of the PPF measures the rate at which his available technology allows him to trade off between two goods. In particular, it represents the opportunity cost of producing an additional unit of good 1, in terms of units of good 2 given up. We call this slope the marginal rate of transformation, or MRT.

As with the other slopes we’re familiar with in good 1 - good 2 space (i.e., the price ratio and the MRS), we will treat the MRT as a positive number, since we know it represents a tradeoff and will (nearly) always be negative.

The curvature of the MRT is clearly related to the nature of the production functions for the two goods. To see how, think of what happens as we move to the right along the PPF. When there’s only one input — labor — this means shifting a single hour of labor from producing good 2 to producing good 1. Since the $MP_L$’s of the production functions measures the amount of output produced by the last hour of labor, it follows that spending one less hour producing good 2 means we give up approximately $MP_{L2}$ units of good 2; and likewise, when we spend one more hour producing good 1, we gain $MP_{L1}$ more units of good 1. Therefore, $MRT = \frac{\Delta x_2}{\Delta x_1} = \frac{MP_{L2}}{MP_{L1}}$ For example, in the derivation of the PPF above we had $x_1 = f_1(L_1) = 2L_1$ $x_2 = f_2(L_2) = L_2$ therefore $MP_{L1} = df_1(L_1)/dL_1 = 2$ $MP_{L2} = df_2(L_2)/dl_2 = 1$ Hence $MRT = \frac{MP_{L2}}{MP_{L1}} = \frac{1}{2}$ Indeed, if you look at the graph of the PPF above, you can see that it has a constant slope of $-\frac{1}{2}$. In other words, when the marginal products are constant, the opportunity cost of producing your first unit of good 1 is the same as the opportunity cost of producing the last (or any other); so the MRT is constant, and the PPF is a straight line.

Optimization in Autarky

Now that we’ve established the constraint Chuck faces, we can talk about his optimal choice. In fact, this is just the same process as maximizing utility subject to a budget constraint, only now Chuck is producing the goods rather than buying them.

All the same techniques for maximizing utility subject to a constraint that we’ve learned so far work here as well, but it’s worth seeing how they apply, especially as we anticipate the model of comparative advantage we’re building up to.

As with finding an optimal bundle along a budget line, we can use a “gravitational pull” argument to find the optimal production choice along a PPF. Intuitively, if Chuck is optimizing, he couldn’t reallocate his time in a way that would make him better.

Think about the following four concepts which shape his decision:

Marginal product of fish $(MP_{L1})$: additional fish per hour spent fishing
Marginal product of coconuts ($MP_{L2}$): additional coconuts per hour spent collecting coconuts
Marginal utility of fish $(MU_1)$: additional utility per fish
Marginal utility of coconuts $(MU_2)$: additional utility per coconut

If Chuck spends an additional hour fishing, he will therefore produce $MP_{L1}$ fish, each of which will bring him about $MU_1$ utils of utility; so his increase in utility from spending another hour fishing is approximately $\frac{\text{utils}}{\text{hour fishing}} \approx MP_{L1} \frac{\text{fish}}{\text{hour fishing}} \times MU_1 \frac{\text{utils}}{\text{fish}}$ Because that hour spent fishing is one less hour collecting coconuts, in that hour he forgoes $MP_{L2}$ coconuts, each of which would have brought him about $MU_2$ utils of utility; so his decrease in utility from spending one less hour collecting coconuts is $\frac{\text{utils}}{\text{hour collecting coconuts}}\approx MP_{L2} \frac{\text{coconuts}}{\text{hour collecting coconuts}} \times MU_2 \frac{\text{utils}}{\text{coconut}}$ He should therefore devote more time to fishing, and less to collecting coconuts, when $MP_{L1} \times MU_1 > MP_{L2} \times MU_2$ If we cross multiply, we can see that this is the same as the condition $\frac{MU_1}{MU_2} > \frac{MP_{L2}}{MP_{L1}}$ or $MRS > MRT$ Conversely, Chuck should devote less time to fishing, and more to collecting coconuts, when $MRS < MRT$.

Fundamentally, this is the same conceptual idea as saying that a consumer should move to the right along their budget constraint if their $MRS$ is greater than the price ratio, and to the left along their budget constraint if their $MRS$ is less than the price ratio. The only difference is that now the slope of the constraint is the MRT, not the price ratio.

Example: Cobb-Douglas Utility

Let’s return to the concrete example above, in which Chuck’s PPF is defined by the equation ${x_1 \over 2} + x_2 = 12$ with its associated marginal rate of transformation of $MRT = {MP_{L2} \over MP_{L1}} = {1 \over 2}$ Now suppose Chuck’s preferences over fish and coconuts could be represented by the Cobb-Douglas utility function $u(x_1,x_2) = x_1x_2^2$ with the associated MRS $MRS = {MU_1 \over MU_2} = {x_2^2 \over 2x_1x_2} = {x_2 \over 2x_1}$ In this case the tangency condition would equate the MRS with the MRT: $\begin{aligned} MRS &= MRT\\ {x_2 \over 2x_1} &= {1 \over 2}\\ x_2 &= x_1 \end{aligned}$ Plugging $x_2 = x_1$ into the PPF and solving gives us $\begin{aligned} {x_1 \over 2} + x_1 &= 12\\ {3x_1 \over 2} &= 12\\ x_1^\star &= 8 \end{aligned}$ Since $x_1 = x_2$, it follows that his optimal bundle is $(8,8)$:

See interactive graph online here.

The “Cobb-Douglas Rule” for a PPF

At the bundle $(8,8)$ above, a quick calculation can show that Chuck is spending 4 of his 12 hours producing fish, and 8 producing coconuts. In other words, he’s using one-third of his resources for fish production.

Recall that for a Cobb-Douglas utility function of the form $u(x_1,x_2) = x_1^\alpha x_2^{1 - \alpha}$ we have shown that a consumer should spend fraction $\alpha$ of their money on good 1, and the rest on good 2, regardless of the prices of the two goods or their income. The utility function above (when normalized, so the sum of the exponents is 1) corresponds to $\alpha = {1 \over 3}$; and indeed, Chuck spends ${1 \over 3}$ of his labor producing fish. In fact, it’s easy to show that this is no accident: in this context, if Chuck has a Cobb-Douglas utility function, he should spend similar fractions of his labor resource on the production of the two goods, regardless of his production technologies or his amount of labor. To see why, we can solve a more general problem. (You’re welcome to skip this section if you just want to trust the formula!)

Let’s think of a labor resource of $\overline L$ hours, and generic linear production functions $\begin{aligned} f_1(L_1) &= A_1L_1\\ f_2(L_2) &= A_2L_2 \end{aligned}$ The derivations we did above imply that the equation of the PPF is ${x_1 \over A_1} + {x_2 \over A_2} = \overline L$ and the MRT is $MRT = {MP_{L2} \over MP_{L1}} = {A_2 \over A_1}$ Because the utility function is well-behaved and the constraint is linear, the optimal bundle will occur at a point of tangency between the PPF and Chuck’s highest possible indifference curve: that is, the tangency condition is $\begin{aligned} MRS &= MRT\\ {\alpha x_2 \over (1-\alpha) x_1} &= {A_2 \over A_1}\\ x_2 &= {1-\alpha \over \alpha}{A_2 \over A_1}x_1 \end{aligned}$ Plugging this tangency condition into the PPF gives us, after some tedious algebra, $x_1^\star = A_1 \times \alpha \overline L$ Now, since $x_1 = A_1L_1$, it follows that $L_1^\star = \alpha\overline L$ In other words, as we expected, Chuck should spend fraction $\alpha$ of his time producing good 1!

Buying and selling coconuts: specialization and trade

Now let’s suppose that Chuck makes contact with the outside world, and finds that there is a market for fish and coconuts: the price of fish is $p_1$, and the price of coconuts is $p_2$. In this model, Chuck’s production choice becomes his endowment of a model like the one we saw last week! He can then trade away from that endowment, either selling coconuts to buy more fish, or selling fish to buy coconuts.

To distinguish between Chuck’s production decision and his consumption decision, let’s write $Y = (y_1,y_2)$ for his choice of what to produce, and $X = (x_1,x_2)$ for his choice of what to consume. It’s easy to see that in making his production decision, since he knows he can buy and sell goods at market prices, Chuck wants to make whatever choice maximizes the market value of $Y$: that is, $p_1y_1 + p_2y_2$.

We can return to a gravitational-pull style argument to analyze his optimal choice. If Chuck spends an additional hour fishing, he will produce $MP_{L1}$ fish, each of which he can sell for $p_1$; so his increase in revenue from spending another hour fishing is approximately $\frac{\text{dollars}}{\text{hour fishing}} \approx MP_{L1} \frac{\text{fish}}{\text{hour fishing}} \times p_1 \frac{\text{dollars}}{\text{fish}}$ Because that hour spent fishing is one less hour collecting coconuts, in that hour he forgoes $MP_{L2}$ coconuts, each of which he could have sold for $p_2$; so his decrease in revenue from spending one less hour collecting coconuts is $\frac{\text{dollars}}{\text{hour collecting coconuts}}\approx MP_{L2} \frac{\text{coconuts}}{\text{hour collecting coconuts}} \times p_2 \frac{\text{dollars}}{\text{coconut}}$ He should therefore devote more time to fishing, and less to collecting coconuts, when $MP_{L1} \times p_1 > MP_{L2} \times p_2$ If we cross multiply, we can see that this is the same as the condition $\frac{p_1}{p_2} > \frac{MP_{L2}}{MP_{L1}}$ or ${p_1 \over p_2} > MRT$ Conversely, Chuck should devote less time to fishing, and more to collecting coconuts, when $p_1/p_2 < MRT$.

The above argument holds true for any kind of PPF. In the special case of a linear PPF, the above argument means that unless $p_1/p_2 = MRT$, Chuck will completely specialize in either fish or coconuts. To see why, let’s return to our concrete example from above.

In the derivation of our first PPF, we said that in one hour, Chuck could produce 2 fish or 1 coconut. If the price of fish is $p_1 = 3$ and the price of coconuts is $p_2 = 4$, this means that he could either make $MP_{L1} \times p_1 = 2 \text{ fish} \times €3/\text{fish} = €6$ producing and selling fish, or $MP_{L2} \times p_2 = 1 \text{ coconut} \times €4/\text{coconut} = €4$ producing and selling coconuts. Since this is true of every hour he has, he should only produce fish.

For more general prices, he should only produce fish if $2p_1 > p_2$, or $p_1/p_2 > 1/2$; that is, if he should produce only good 1 if $p_1/p_2 > MRT$!

The following graph illustrates this point. Bundle $Y$ is Chuck’s production choice; the green line passing through it is all the other bundles which the same monetary value. Try moving $Y$ along the PPF to see how Chuck can maximize the value of what he produces. Then, change the prices, and see how his optimal production choice changes!

See interactive graph online here.

The gains from specialization

Once Chuck has made his production decision, the value of what he produces determines a budget that he can use to buy fish and coconuts: in other words, the green line in the diagram above becomes his budget line.

As we saw before, Chuck will maximize his value of production by specializing in one good or another. If Chuck has specialized in producing only fish, and produces $y_1 = 24$ fish, the monetary value of that decision is $24p_1$. Therefore, his budget line would be defined by the equation $p_1x_1 + p_2x_2 = 24p_1$ On the other hand, if he has specialized in producing only coconuts, and produces $y_2 = 12$ coconuts, that would earn him $12p_2$, so his budget line would be $p_1x_2 + p_2x_2 = 12p_2$ As long as he completely specializes in the more profitable good, his budget line will lie above his PPF: that is, he will be able to afford bundles with more of both fish and coconuts than if he had relied on only his own production! This makes him better off, because he can consume a bundle which gives him higher utility:

See interactive graph online here.

These are the famous gains from specialization that are at the center of the Ricardian model of trade. However, to get the full version of that model, we have to look at what’s going on with the other people in the model: that is, the ones Chuck is trading with. And, we have to figure out where these prices are coming from.

Absolute and Comparative Advantage

Let’s now move beyond a single agent, but to keep things simple let’s suppose that there is only one other person in this model, who can also produce fish and coconuts: another marooned agent named Wilson. (Yes, I know Wilson is a volleyball, and can’t produce anything. Work with me here, we need another agent.) Wilson also has $\overline L = 12$ hours, but is more productive than Chuck in producing both goods: he can produce 3 fish or 3 coconuts per hour! Therefore, he can produce at most 36 fish, or 36 coconuts. You can see his PPF, alongside Chuck’s for comparison, in the diagram below:

See interactive graph online here.

Because Wilson can produce more fish per hour than Chuck, we say he has an absolute advantage in the production of fish; likewise, for the same reason, he also has an absolute advantage in the producing of coconuts.

It might be tempting to think that Wilson has no possible gains from trade with Chuck, because he has an absolute advantage in both goods; but this isn’t the case! Remember that the MRT measures the opportunity cost of fish, in terms of coconuts. As we showed before, Chuck can produce a fish giving up only half a coconut; Wilson, on the other hand, must give up an entire coconut for every fish he produces. Because Chuck can produce fish at a lower opportunity cost (in terms of coconuts) than Wilson, we say that Chuck has a comparative advantage in the production of fish. Likewise, Wilson’s opportunity cost of a coconut is one fish, while Chuck’s is two fish; hence Wilson has a comparative advantage in the production of coconuts.

Productive Pareto Efficiency and Specialization

When we spoke of Pareto efficiency in the Edgeworth Box in Lecture 2, we were speak of allocative efficiency: that is, we couldn’t reallocate the consumption of goods among agents without making one of them worse off.

When we’re thinking about Chuck and Wilson’s production decisions, we can similarly talk about productive efficiency. In particular, we say that a joint production decision is efficient if we couldn’t reallocate resources to produce more of at least one good without making less of any goods.

For example, suppose both Chuck and Wilson were evenly distributing their labor between fish and coconuts. This would result in Chuck producing 12 fish and 6 coconuts, and Wilson producing 18 fish and 18 coconuts; therefore, between them, they would produce 30 fish and 24 coconuts. We can see this choice as an allocation in an Edgeworth Box with those dimensions, as shown below:

See interactive graph online here.

However, this isn’t the biggest possible Edgeworth Box! We’ve established that Chuck has a comparative advantage in fish (good 1), and Wilson has a comparative advantage in coconuts (good 2). Suppose, then, that Chuck produces 6 more fish, and Wilson produces 6 fewer. If you drag the dots in the diagram above, you can see that while they’re producing the same amount of fish, they’re now producing 3 more coconuts…so the Edgeworth Box has grown in size!

Let’s take this one step further: suppose we say that Chuck and Wilson together would like to produce 30 fish. What is the maximum number of coconuts they could produce?

If we repeat the exercise above, we can see that they can get another 3 coconuts if Chuck produces 6 additional fish, and Wilson produces 6 fewer. But at this point Chuck is producing his maximum number of fish (i.e., he is completely specializing in fish), while Wilson is producing 6 fish and 30 coconuts. Therefore, if they want 30 fish, they can collectively have at most 30 coconuts; and they do so by Chuck specializing in fish, and Wilson dividing his time between fish and coconuts.

In fact, we can do this for any quantity of fish the two of them can produce. De-select “Show Edgeworth Box” and select “Show joint PPF” in the diagram above. This shows the set of combinations that Chuck and Wilson can achieve, if they are being productively efficient. And in fact, what you can see is that to get to the joint PPF, at least one of the two must be specializing in the good for which they have comparative advantage:

If they both specialize (Chuck produces only fish, and Wilson only coconuts), the produce at the point $Y = (24,36)$ – i.e., the kink.
If Chuck specializes and Wilson mixes, they produce along the orange portion of the joint PPF to the right of the kink. Along this segment, the MRT is 1, which is Wilson’s MRT, because producing another fish requires Wilson to fish a bit more and collect coconuts a bit less.
If Wilson specializes and Chuck mixes, they produce along the blue portion of the joint PPF to the left of the kink. Along this segment, the MRT is ${1 \over 2}$, which is Chuck’s MRT, because producing another fish requires Chuck to fish a bit more and collect coconuts a bit less.

Finally, there’s one last way to analyze the efficiency of a production decision. Check the box labeled “Show PPFs in the Edgeworth Box;” this will show the PPFs in the Edgeworth Box diagram, with Chuck’s origin being the bottom-left corner and Wilson’s the top-right. Note that when Chuck and Wilson are producing at a point along their joint PPF, the PPFs don’t overlap in the Edgeworth Box! Can you figure out why that is?

Competitive Equilibrium with Complete Specialization

OK, all the above was a lot of text to teach you something you probably learned in Econ 1, or high school: that it’s efficient for people to specialize in what they have a comparative advantage in. It’s one of the most fundamental lessons of economics.

But will people do so? We established before that an agent will produce only good 1 if their opportunity cost of producing good 1 is less than the price ratio: that is, $MRT < p_1/p_2$. Suppose we wanted Chuck and Wilson to completely specialize: that is, we wanted Chuck to produce only fish, and Wilson to produce only coconuts. In that case we would need Chuck’s MRT to be less than the price ratio, but Wilson’s MRT to be greater than the price ratio. Because Chuck’s MRT is ${1 \over 2}$ and Wilson’s is 1, this means we need ${1 \over 2} < {p_1 \over p_2} < 1$ For prices in this range, both of them will want to specialize, as we can see in the following diagram:

See interactive graph online here.

But which of those prices will occur? Let’s assume both Chuck and Wilson have the utility function $u(x_1,x_2) = x_1x_2^2$, and think about their supply and demand for fish. For simplicity, let’s assume $p_2 = 1$, and calculate their demand for good 1 as a function of $p_1$.

When both Chuck and Wilson specialize, we’ve established that Chuck is producing $y_1^C = 24$ fish and Wilson is producing $y_2^W = 36$ coconuts. Therefore the monetary value of Chuck’s fish is $m^C = 24p_1$, while the monetary value of Wilson’s coconuts is $m^W = 36$. Using the Cobb-Douglas trick, we know that each of them will spend ${1 \over 3}$ of their money on fish. Therefore their (gross) demands for fish are $\begin{aligned} x_1^C(p_1) &= {m^C \over 3p_1} = {24p_1 \over 3p_1} = 8\\ x_1^W(p_1) &= {m^W \over 3p_1} = {36 \over 3p_1} = {12 \over p_1} \end{aligned}$ Therefore, Chuck’s net supply curve is perfectly inelastic at $24 - 8 = 16$, and Wilson’s net demand curve is $d^W(p_1) = {12 \over p_1}$. Equating supply and demand gives us $\begin{aligned} s^C(p_1) &= d^W(p_1)\\ 16 &= {12 \over p_1}\\ p_1^\star &= {12 \over 16} = 0.75 \end{aligned}$ And indeed, if we look in the Edgeworth Box, we can see that this is indeed the price ratio that causes each of them to want to trade to the same place in the Edgeworth Box:

See interactive graph online here.

Summary and next steps

In this lecture we saw one way that a particular location in the Edgeworth Box might arise, with linear PPFs and complete specialization. Essentially, we used the Edgeworth Box framework, as well as our analysis of indifference curves and consumer optimization, to deepen your understanding of the classic Ricardian model of comparative advantage.

However, linear PPFs and complete specialization are a pretty rudimentary and simplistic way to analyze the real world. To wrap up this unit, we’re going to look at the notion of incomplete specialization.

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