Worked free response question on unemployment | APⓇ Macroeconomics | Khan Academy

We are told the following table shows labor market data for country X, and they tell us how many are employed, frictionally unemployed, structurally unemployed, cyclically unemployed, and also not in the labor force.

So this first question here, and actually we skipped part A because we want all of these to focus on our labor force, so calculate the unemployment rate in country X. Show your work.

So pause this video and see if you can work through that.

All right, so our unemployment rate is going to be equal to our number unemployed, which is going to be the sum of the friction unemployed, structure unemployed, and cyclically unemployed, divided by our total labor force.

So our labor force is going to be our employed plus unemployed. So it's going to be number employed, employed, plus number unemployed, unemployed. We want to express this as a percentage. Since they're asking us to show our work, we could even put that there times 100. It never hurts to give more clarity when someone asks you to show your work.

So what's this going to be? Our number unemployed is going to be ten thousand plus five thousand plus five thousand. Actually, let me just write this: 10k plus 5k plus 5k over our employed is 180k, and then our number unemployed is going to be plus 10k plus 5k plus 5k times 100.

This is equal to—in our numerator we have 20,000. I'll just write it out here: twenty thousand. Our denominator we have two hundred thousand, two hundred thousand times one hundred percent.

So this is going to—all this is going to be 0.10, and then times 100, this is going to be equal to a 10% unemployment rate.

All right, now part C: calculate the labor force participation rate in country X. Show your work.

So once again, pause the video and see if you can figure that out.

So let's just remind ourselves what our labor force participation is. It is going to be our labor force, we could say number in the labor force, and then over our total eligible population.

So you could say number in—or so I would say labor force, labor force plus not in labor force, plus the number not in labor force. You might say, well, when you're this denominator is the eligible population, who's not eligible? Would be people who are not of working age. It might be people who are incarcerated or institutionalized in some way. It could be people in the military.

So then, and of course we want to express this as a percentage. So right times 100 percent is equal to...

So our labor force is going to be all of the employed or unemployed people. So this is going to be—it's essentially this denominator right over here. So it's going to be 200,000—that's our labor force—divided by our labor force, which is 200,000, plus the not in the labor force. So that's 100,000, and of course times 100 percent.

This is going to be equal to two-thirds times 100 percent. So we could write 66.7. It would be 66.6 repeating, but 66.7 percent is our labor force participation rate. Fair enough.

Now part D: draw a correctly labeled graph of the production possibilities curve for country X with consumer goods on the horizontal axis and capital goods on the vertical axis. Indicate a point on your graph labeled Z that reflects the current level of unemployment.

Pause your video and see if you can do that.

All right, now let's do that together. I'll scroll down a little bit so I have space to do that.

So they tell us with consumer goods on the horizontal axis. So let me do it like that. My horizontal axis I am going to have consumer goods. Consumer goods.

Then they say capital goods on the vertical axis. So it might look something like this: this is capital goods, capital goods on my vertical axis, and it's the production possibilities curve.

So they typically look something like this. Now they say indicate a point on your graph labeled Z that reflects the current level of unemployment.

So this is very interesting. You might say, hey, it's a point on my graph. Maybe I need to put it on this curve someplace, and that would not be the case here because we have some level of cyclical unemployment.

You see it right over here: cyclical unemployment. We are producing below our potential, I guess is one way you could say it. So that means we would be behind the production possibilities curve.

So that point labeled Z—labeled Z—I'd put it someplace behind the curve, and to get credit for this, anywhere behind the curve would suffice. So you could put it right there, our point Z.

Since they're asking us to show our work, and it's always good to do things properly, if they're grading this on an AP test, for example, you would get points. It's always good to put a title too, so you could say production possibilities curve for country X.

And we're done.