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” s understand the intuition of search theory in this video. And we ll do it it with an example so suppose we re looking for a job and that job anywhere between zero to 100. And let s say at the moment. We found a job that s 50 now.
The question would be what would be the benefit of looking for another job. So looking for another job and giving us a benefit means that we would like to have a higher wage. But we don t know for sure that that s going to happen since we have to look for it we don t know what s gonna happen in the future. So we re dealing with uncertainty.
We re dealing with uncertainty. This is the this is from the topics in microeconomics that we work with uncertainty now a signal in our mind. When we work with uncertainty has to be that we re going to work with probability so we have a probability that our wage can be greater than 50. And because we re dealing with probability.
What we want to calculate is something in expectation. So we want to calculate the expected benefit of having a wage higher than 50. And the reason we call it expected and not just pure benefit..
It s because this is uncertain. We don t know for sure that this benefit is going to happen so the expected benefit is the probability times. That benefit of that specific outcome now how would that look like over here. We re at 50 and we would like to have a wage higher than 50.
So we would like a wedge between 50 and 100 so somewhere in this range over here. But we said that this is uncertain. We said that we need to know the probability so how can we find the probability of this event of this outcome of having a wage higher than 50 well the probability is the same as proportion. Which means that we are looking for the proportion of this shaded area.
Now. What is a proportion a proportion is the ratio. What kind of ratio this specific length relative to the entire length. So.
The proportion would be in this case. 100. Minus 50..
100. Minus 50 relative to 100 minus 0. Zero. So.
That s 50 over a hundred. And that s equal to one over two so we have a one over two or a fifty percent chance of finding a job higher than 50. And intuitively if we look even on the graph that makes sense because from fifty to a hundred that s half way through as it goes from all this graph so halfway means. 50 of it so this probability makes sense.
Now let s have a look. What would be the expected benefit and to know the expected benefit. We must know what kind of wage can we expect like what what what what kind of wage could be higher than fifty now what s our best guess because this is again uncertain. This is uncertain so we must know how to estimate this new wage this higher wage.
We have no reason to think that that higher wage could be 51 or 57 or 94. And so on so the best guess without having an information is to take the average. Now..
The question is what kind of average well the average would be in this case. The midpoint the midway through fifty to a hundred also we call it the median. So if we take the middle point or the median as we say between these two points. That would be the best guess for our higher wage that would be the average wage that we can expect to have so this would be our best guess now what is this median.
What is this middle point well the middle point between 50 and 100 would be 75. Because it s 25 from 125 from 50. Now that would be our best guess. But we are talking about the benefit.
What s the benefit of having a wage higher than 50. Well. If we would have a wage of 75 causing an expectation. We we expect that 75 minus 50.
Gives us an additional 25 dollars. And that would be our benefit. So we re speaking about this area over here that could be our benefit..
So our benefit would be 25 dollars. But we also know that that s not for sure. There s only a 1 over 2 probability to happen so if we take all this into a into a summary. Then the expected benefit would be the probability times.
The benefit. Which means that the expected benefit would be the probability of 1 over 2 times this potential benefit from having a higher wage and out equal to 12 point 5 dollars. So in expectation by taking into. Account the.
Probability we might have a gain a benefit of 125 dollars. ” ..
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