Consider a market where supply and demand are given by qxs...

Consider a market where supply and demand are given by QXS = -18 + PX and QXd = 81 - 2PX. Suppose the government imposes a price floor of $38, and agrees to purchase any and all units consumers do not buy at the floor price of $38 per unit. Assume that the government simply removes product from the market through its purchase. a. Determine the cost to the government of buying firms' unsold units. $____ b. Compute the lost social welfare (deadweight loss) that stems from the $38 price floor. $____

Transcript

00:01 This is a question about price floors, but we start off with a supply curve of minus 18 plus p and a demand curve of 81 minus 2p.

00:11 And we're thinking about a price floor.

00:14 So the first thing i want to do is to invert these things, right? i want to invert them to get a better idea of what the situation looks like.

00:22 So i could say that the price is equal to a quantity supply plus 18 or that, sorry, two.

00:30 Times the price is equal to 81 minus qd or price is equal to 40 .5 minus qd over two.

00:40 So if i sketched this in terms of quantity and price, the demand curve starts at 40 .5 and the supply curve is going to start at 18, right? the equilibrium looks like the market looks like this.

00:58 So at equilibrium, we know that quantity supplied is equal to quantity demanded.

01:04 So i can say minus 18 plus p is equal to 81 minus 2p.

01:10 3p is equal to 99.

01:14 P is equal to 33.

01:16 So here's 33, but the price floor is going to be at 38.

01:24 So in equilibrium, the quantity demanded is going to be low and the quantity supplied is going to be high, right? there's going to be a surplus.

01:35 So we need to figure out how much the government has to buy, right? we have to determine what's going on here, right? the surplus that the government has to buy, well, let's think about the quantity supplied at 38.

01:54 This is equal to minus 18 plus 38 is equal to 20.

01:59 The quantity demanded at 38 will be 81 minus 2 times 38, which is equal to 5, right? 76, yeah, 5...

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