# am i missing the point with Demand functions? (dont understand them at all!) watch

1. could somebody explain the following in english? would be most grateful, thanks

• Market demand function, Q(p)

if linear Q = a – b p

• Market inverse demand function, p(Q).

if linear p = a/b – 1/b Q
2. Q(p) is a function (like f(x) ) where quantity Q depends on price p...this is the demand funcation.

If you think about what a demand curve looks like, it's a downward sloping line like y = 50 - x, on an x and y axis, well on a price quantity diagram it can be rewritten as Q = a - bp (as price p increases, Q will get smaller, therefore it's downward sloping), where a is where it crosses the y axis and where -b is the negative gradient (it is downward sloping).

The inverse demand function p(Q) is where you rearrange the demand function to get a function where price depends on quantity (rather than quantity depending on price).

To get the inverse you just rearrange to make p the subject...

3. aha, thanks. One question though why in the final equation do they write it as p = a/b – 1/b Q? Whats the point of writing 1/b with a Q on the outside rather then q/b?

Also, any idea what this means? I kinda understand it but putting the letters on the outside confuses me. Its about nash equilibriums/bertrand competition.

NE -> p1 ≈ c2, profit1 ≈ (c2– c1 )Q(c2) > 0

q2 = profit2 = 0

thanks again

EDIT: The whole text:

asymmetric costs --> c1 < c2

The high-cost firm will never set a price below its marginal cost c2
For prices greater than c2, undercutting as in the symmetric case
When prices arrive at c2, the low cost-firm can still undercut the rival’s
price by a small amount, and steal all market

NE -> p1 ≈ c2, profit1 ≈ (c2– c1 )Q(c2) > 0

q2 = profit2 = 0

Market power (low-cost firm’s mark-up) ≈(c2-c1)/c2

It can be very small if the difference in costs is small

Concentration --> max degree (only the low-cost firm is active)
4. (Original post by redkopite)
aha, thanks. One question though why in the final equation do they write it as p = a/b – 1/b Q? Whats the point of writing 1/b with a Q on the outside rather then q/b?
They're the same thing. It's like saying instead of .
Also, any idea what this means? I kinda understand it but putting the letters on the outside confuses me. Its about nash equilibriums/bertrand competition.

NE -> p1 ≈ c2, profit1 ≈ (c2– c1 )Q(c2) > 0

q2 = profit2 = 0

thanks again

EDIT: The whole text:

asymmetric costs --> c1 < c2

The high-cost firm will never set a price below its marginal cost c2
For prices greater than c2, undercutting as in the symmetric case
When prices arrive at c2, the low cost-firm can still undercut the rival’s
price by a small amount, and steal all market

NE -> p1 ≈ c2, profit1 ≈ (c2– c1 )Q(c2) > 0

q2 = profit2 = 0

Market power (low-cost firm’s mark-up) ≈(c2-c1)/c2

It can be very small if the difference in costs is small

Concentration --> max degree (only the low-cost firm is active)
Sorry I haven't done that yet... so I guess you're at uni now? Where are you studying?
5. lol yeah am at leicester cool will try a separate post for the bertrand competition thing, thanks for all the help!

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