equilibrium price and quantity

CFA Level I
#1

Question: Consider a market where quantity demanded - 1500 - 3x price, and quantity supplied = 2000- 5xPrice. With respect to equilibrium price and quantity, there is:

  1. no market equilibrium

  2. a stable market equilibrium

  3. an unstable market equilibrium

For this type of probelm, I sometimes get it right and sometimes get it wrong. So I must be using wrong method.

Can someone teach me the best way to solve this?

Thanks a lot.

#2

There is an equilibrium. To determine it, set supply equal to demand and solve for price:

1,500 – 3p = 2,000 – 5p

2p = 500

p = 250

q = 1,500 – 3(250) = 750

(Check: q = 2,000 – 5(250) = 750. Bingo!)

To determine whether it’s stable or unstable, check what happens when the price is above (or below) the equilibrium price: for a stable equilibrium, if the price is above the equilibrium price, quantity supplied should exceed quantity demanded, and if the price is below the equilibrium price, quantity demanded should exceed quantity supplied; vice-versa for an unstable equilibrium.

If the price were, say, 300, then:

D(300) S(300) = 2,000 – 5(300) = 500 units

S(300) D(300) = 1,500 – 3(300) = 600 units.

So, when the price is above the equilibrium price, supply _ demand _ exceeds demand _ supply _, so the equilibrium is stable _ unstable _.

You should check that when the price is 200 (less than the equilibrium price), D > S.

#3

Thanks, clearly understood !

#4

My pleasure.

Good to hear.

By the way, the easy way to remember which equilibrium is stable and which is unstable is to look at normal (upward sloping) supply and (downward sloping) demand curves: that equilibrium is stable, higher prices lead to excess supply, and lower prices lead to excess demand.

#5

I believe that you may have made an error.

To begin with, the supply curve is downward sloping (note the negative coefficient) and as such, it makes it less likely that the equilibrium is stable. Note that the equation I highligthed above is incorrect (i.e. you may have mixed up the demand and supply equation): -

Qd = 1500 - 3p,

Qs = 2000 - 5p

S(300) = 2,000 – 5(300) = 500 units

D(300) = 1,500 – 3(300) = 600 units

Supply is actually less than demand when prices increase.

#6

As a rule of thumb though, just look at the coefficient of price (at least for linear equations).

  • The coefficient of price should be negative for demand (just so you get a nice downward sloping curve) and;
  • the coefficient of price should be positive for supply (just so you get a nice upward sloping curve)

I don’t really have the L1 materials in front of me now but I tend to associate stable and unstable equilibrium with the cobweb model (usually depends on the steepness of the demand and supply curve) myself…

#7

I did, indeed, confuse the formulae. Thanks for the sharp eye.

I’ve corrected it.

#8

I figure that most candidates aren’t connoisseurs of linear algebra, so they’d rather not have to memorize a rule about slopes. It’s a simple matter to check as I outlined above.

#9

This isn’t a probability problem: what is more likely or less likely doesn’t really matter; what matters is whether it is, _ in fact _, stable or unstable.

When both curves slope downward (or both slope upward), that tells you that you need to check whether it’s stable or nor, whereas if the supply curve is normal (upward sloping) and the demand curve normal (downward sloping), you needn’t check it: it’s stable.

#10

But it is just checking whether the coefficient of price (or quantity, depending on the question) is positive or negative surprise

  1. If your demand curve has a positive slope, you will most likely get an unstable equilibrium
  2. If your supply curve has a negative slope, you will most likely get an unstable quilibrium

Of course, the cobweb model is slightly more complex but if I remember correctly, it isn’t tested in the CFA economics syllabus (I may be wrong though).

#11

Sorry about that. The CFA syllabus has made it a habit for me to say “most likely” and “least likely” even though it really should be “definitely” and “not a snowball’s chance in h**l” :stuck_out_tongue: Call it “covering my a**” syndrome, if you must :wink:

However, the other reason I say “most likely” is because when the supply curve has a downward slope, it is theoretically possible to have a stable equilibrium (say, in a backward bending labour curve since only a certain portion of the curve would be downward sloping) but that is probably not in the CFA syllabus. I help around with tutorial for certain undergraduate economics where these sort of unlikely stuff get asked every now and then. Therefore, I tend to overthink economics questions (though fortunately not when I sat for the exams) and forget what is in the syllabus and what is not in the syllabus.

#12

@Kelly Z

Ignore whatever I typed (as it will probably confuse you more) and just reread the second post in this thread.