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A market is described by the following supply and demand curves:$$Q^S = 2P$$ $$Q^D = 300 - P$$a. Solve for the equilibrium price and quantity.b. If the government imposes a price ceiling of \$90, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?c. If the government imposes a price floor of \$90, does a shortage or surplus (or neither) develop?What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?d. Instead of a price control, the government levies a tax on producers of \$30. As a result, the newsupply curve is:$$Q^S = 2(P - 30).$$Does a shortage or surplus (or neither) develop?What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?
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That was not easy, glad this was able to help
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This will help alot with my midterm
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okay. And this question we're giving a market described by the following supply and demand functions where the quantity supply it e equals two times the price and the client demanded equals three hundred minus the price. The first thing that we want to figure out is equilibrium pricing quantity. Well, we know that the equilibrium price is such that quiet supplied should equal quantity demanded at that price. So in order to find this price, all we need to do is set client supplied equal to the client demanded. And we have those two functions here. So we'LL say to p equals three hundred minus peak and then just adding people size we'LL have three p equals three hundred and we'LL find that the equilibrium price is one hundred. From this, we can also plug in the equilibrium price to either the quantity supplied or demanded to arrive at the equilibrium quantity, and I'm going to plug it into the demand function this time. So I will do three hundred minus the equipment price of one hundred and we will arrive at an equilibrium quantity of two hundred. And of course, you could also multiply to buy one hundred and arrive at the same equilibrium quantity. So that's party for apartment B. We're going to impose a price ceiling which I call P Max of ninety. Now, recall that the equilibrium price currently is one hundred. We're going to impose the maximum price below equilibrium price such that you can't engage in market activity above a price of ninety. And so we can tell by visual inspection alone that this is going to influence equilibrium behavior in particular, we should end up with quality supplied Ah, less than quantity demanded. So I'm gonna plug in this price ninety two the quality supplied we'LL just have to times ninety equals one hundred eighty and then I will also plug in this price of ninety two the demand function we'LL have three hundred minus ninety renders the quantity demanded to be two hundred and ten So we see the exact behavior that we expect to see and in particular we know that wouldn't quality supplied is less than client demanded. There are more people interested in purchasing the good thing that good is available In this case we have what's known as a shortage and the magnitude this shortage is just going to be our two hundred ten minus one eighty. So we have a shortage of thirty now in part. See, we're going to institute a price floor at ninety. Now, when we have a price floor below equilibrium price, We know that this is going to be an ineffective price control because what a price floor ninety is saying is we can sell at or above this price ninety, in which case equilibrium solution is uninterrupted. So we're just going to arrive at the original price and the original quantity that we saw Foreign Party once again, because equilibrium behavior is not influenced by an ineffective price control. And then finally, in Part D were saying instead of a price control, the government loves attacks on producers of thirty dollars. This is just going to change supply curve in the following way. Instead of having just client supplied equals to pee, we now have client supplied equals two times the quantity p minus thirty. Well, since this is just influencing the shape of the Speicher for not goingto have either shortage or surplus is just going to influence the equilibrium solution. So doing the same approach that we did in part a I'm going to set Qantas supplied equal to quantity, Demanded to find Q star in peace star So we have two times the quantity. I'm just gonna multiply this out here. We're gonna have to pee. Minus sixty equals. Still just the original demand function three hundred minus p and then putting the piece on this side and the images on the other side we're gonna have three p equals three sixty, which will give us that piece Star equals one twenty and then in the exact same way as in part A. I'm just gonna plug in this piece, start either the two equations This time I'll do the supply equation And so we'll have that key star equals two times one twenty, minus sixty And that will give us two forty here minus sixty, So we will have equivalent quantity of one eighty And this is true for both the quantity supplied and the quantity demanded
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