jalen said:
okay, for the 20 cents one you just need to make 20 equal to the equation on the left, right?
20=-20+0.50Q
40=0.50Q
80=Q
I hope that's right...can someone help me check.
Well, that's right, but if I was you, I'd plug 20 cents into both functions to see what results. I think that gives one a clearer sense of the whole story.
For demand you get:
20 = 200 - 1.25Q
-180 = -1.25Q
Q = 144
For supply you get:
20 = -20 + 0.50Q
40 = 0.50Q
Q = 80 (which is exactly what you got)
The important thing is to not just go through the problems and numbers, but rather to understand exactly what's going on economically. Notice in this case, that at that price consumers want 144 oranges, but suppliers are only willing to produce 80 oranges. Again, the short side wins out, so 80 is the quantity that will be produced. Notice that this is a shortage (as opposed to the last example which was a surplus). Pretend for a minute, that each orange will be purchased by only one person, and notice what this means, that at 20 cents only 80 people will get oranges and the other 64 people (144 - 80) who wanted an orange at that price will go home empty handed. Also, think to yourself, if the oranges won't be allocated solely by the price system, then how will you allocate 80 oranges to 144 people? In other words, how will it be decided who will get them? Some potential answers are, that it will be "first come first server," or people who have social connections with the producers will get first dibs, or that the producers will be more inclined to give to those they like more (potentially based on race, gender, or some other criteria), or that consumers will have to bribe the producers by offering an amount of money above the 20 cent legal price.
Although it's a simple example, it's very powerful and has many real world applications. The goal of economic theory (or any theory for that matter) is to derive refutable propositions (so that they can be tested empirically). One of the powerful testable propositions that is derived from this theoretical model, is that price controls will have predictable effects. Such models predict that controls on gas prices and rent controls lead to long waiting lines, poor customer service, and often times many people will not receive the good even after waiting in line for long periods of time. Such models also predict that minimum wage legislation will lead to higher unemployment rates. There's many more predictions, but these were the first that came to mind, as they've been analyzed extensively.
