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Alright this last little video on the First and Second Welfare Theorem has a figure pretty
similar to the last one except now we have the Competitive Equilibrium budget line. It
goes through the original endowment. Recall for this economy that the relative price is
proportional to the ratio of the total amount of y to total amount of x. Right now that's
148/120, which is an ugly fraction, which explains why this allocation does not have
a nice integer value to it. So I'm going to make the total endowment of the economy equal
in x and y. So let's make the y value 130 and let's make the x value 130. So that will
make the equilibrium relative price 1. And now I see this is a nice integer value over
here. Okay! And so let me show that now we only have the ability to move the red dot
along the budget line. So that's a lot of x. We can lower the amount of x on the budget
line but then therefore increase the amount of y. And since the relative price is 1 you
should note that 62 plus 36 adds up to 98. So does 25 plus 73. So we're staying on the
budget line as we lower the amount of x. So here's a proposed trade to 59,39.
Let's in fact do what we did in the previous diagram. Let's move the initial allocation
out of this proposed trade 59,39. So moving x to 59 and then we're going to move y to
39. And it may not be obvious till we're done here but this is back on the original budget
line. Now the indifference curves are still crossing here but the lens is very small.
Looks like if you lower the amount of x a little bit and increase the amount of y you'll
make them both better off. So let's try doing that. See it says "A approves the trade."
So let's move us... What's happening here? There we go. So we're at 52,46. And let's
try even going a little further 51, 50,48. Let's try that. And let's try, in fact I know
that's the actual competitive equilibrium. So let's move this thing to 49,49. This is
the competitive equilibrium allocation.
So I'm going to move x to 49 here. And I'm going to move it to 49 over here. And let's
take a look at what it looks like when we're done. There we are. And notice what happened.
The budget line is tangent to the indifference curve through this point. And the indifference
curves are tangent to each other. So the First Welfare Theorem says at the competitive equilibrium,
since both indifference curves have to be tangent to the budget line, they are tangent
to each other. So the Competitive Equilibrium is Pareto Optimal. The Second Welfare theorem
says the reverse. If you start with a Pareto Optimum and the indifference curves are tangent,
you can find the budget line that actually is the common tangent. And therefore there
are prices that support that Pareto Optimum as a Competitive Equilibrium.