Demand function?

Question

The demand function for x is D(p)=65-2p and the supply function is S(p)= 20+p. The price that should be set to restrict the quantity supplied to 30 units is closest to:
a) $5
b) $10
c) $15
d) $50
e) $55

I'm thought this was a trick, otherwise I would have just plugged in for p in the supply equation. Any ideas?

Answer 1

Some varying answers here, I'll give it a shot, and I'll try to be clear and go over my steps.

My answer is b) $10.

I like to start out all problems of this sort (when I don't have a time constraint) by finding the optimal P and Q. Typically when asked these questions, they will be in relation to the social equilibrium, so it is a step you will usually do anyway. Even if you don't, it's a useful way of checking to see if your answers don't make economical sense.

The optimal amount comes at the price and quantity where the supply and demand curves intersect. At this point, price and quantity will be the same for both curves.

So we set Qd = Qs, or 65 - 2P = 20 + P --> 3P = 45, so P = 15. This is our optimal price. The optimal quantity can now be found simply by plugging this value into either equation: S(15) = 20 + 15 = 35.

So we know that, optimally, the market demands 35 units at a price of $15.

Now when we place price restrictions on products, it does not affect the demand curve nor the supply curve, at least in the short run. In this scenario, restricting a quantity will require a price ceiling, in other words, lowering the price so that producers supply less of the product. To find this price, we need to analyze NOT the demand curve, but the supply curve... when will producers produce only 30 units?

Our equation is already set up with price as the variable, so we just plug in the 30 = Qs = 20 + P, and we can find that our answer is $10.

Note: at P = $10, Qd = 65 - 2(10) = 45, so there will be a shortage of (45 - 30) = 15 units.

Hope that helps.

Answer 2

set the demand function and supply function equal to eachother and then solve for p. So your equation is:

65 - 2p = 20 + p

p is equal to $15, which is the equilibrium price. However, the quantity supplied must be less than 30 units. At $15 the quantity supplied is 35 units, which is too many units. So the price would need to be set at $10, where exactly 30 units would be supplied. B is your answer.

Answer 3

I say C) $15.

You want to restrict supply to 30, which is the same as restricting Demand to 30 (firms will keep supplying the market as long as there is demand).

D(p) = 65 -2p
30 = 65 -2p
35/2 = p
17.5 = p

So the closest you can do with the options given is C.

Answer 4

S= 20 + p
you want to force S = 30
so you are right plug S=30
30 = 20 + p
find p
unless you didn't put all the information here it is as easy as it gets