Economics - demand curve, price and equilibrium

jalen

Suppose the demand curve for apples is P=800-2Qd. Where P is the price per pound(in cents) of an apple and Qd is the quantity demanded per year(in millions of pounds). Suppose that the supply curve for apples is: p=-300+3Qs. Where P is the price per pound(in cents) of an apple and Qs is the quantity supplied per year(in millions of pounds).

a) Calculate the equilibrium quantity and price of apples.

800-2Q=-300+3Q
1100=5Q
Q=220

Demand: 220=800-2Qd
-580=-2Qd
Qd=290

Supply: 220=-300+3Qs
520=3Qs
Qs=173

Please check if my calc are correct =)

b)Suppose the government puts in a price floor of $4.50 per pound on apples. How big will the surplus of apples be? Show your work.

I'm not sure about this question...would you just make the $4.50 equal to one of the above equations?

c)Suppose the government puts in a price ceiling of $2.50 per pound on apples. How big will the shortage of apples be? Show your work.

.....and same thing for this one?

EnumaElish

a) Q = 220 is the equilibrium quantity common to both demand and supply. If you substitute 220 into either Qd or Qs the result will be the equilibrium price (again, common to demand and supply).

b) You would put 450 cents on the left-hand side of both equations, then solve for Qd and Qs separately. The difference Qs - Qd is the surplus.

c) Same idea as in b, except the shortage is Qd - Qs.

Economist

Yeah, this part looks right.

You made a mistake here. You already found quantity (Q) in part one, so now you need to find price (P). So plug in Q=220 (found in part a) and solve for P. You plugged in P=220 and solved for Q (which is backwards).

Again, you mixed up your variable. You already found Q, so you need to find P.

Essentially, you are trying to find an equilibrium P and Q so they will be the same whether you use the supply or demand functions. Essentially, you are finding the intersection point of two lines.

On this problem you will use P=450 and solve for Qs and Qd. Since we are not in equlibrium this time, Qs and Qd will not be equal.

In this case you'll need to use a little intuition. If you want 3 cheeseburgers at a price of $2, but McDonalds wants to sell you 10 cheeseburgers at a price of $2, how many cheeseburgers will you purchase? Apply this same logic to the question above.

You can calculate the surplus by finding the area of the "dead weight loss." It will help to draw a graph.

Same process as part b, and again you'll need to use some intuition to figure out what's going on. In this case, lets say that cheeseburger are $1 and you want to buy 5 of them, but McDonalds only wants to sell 2 of them, how many will be sold?

Again you will also have to draw a graph and calculate the area of a triange.


Try the problems again, and then type in your answers. I will check them for you to see if they are correct.

jalen

b)Demand 450=800-2Qd
-350=-2Qd
Qd=175

Supply 450=-300+2Qs
750=3Qs
Qs=250

Qs-Qd
250-175=75


c) Demand 250=800-2Qd
-550=-2Qd
275=Qd

Supply 250=-300+3Qs
550=3Qs
183.3=Qs

Qd-Qs
275-183.3=91.7

Also, is the graph suppose to look similar to an AS AD curve?

Economist

The numbers look correct.

The graph will be a supply and demand graph.