Hey there! Sign in to join this conversationNew here? Join for free

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

    • Thread Starter
    Offline

    1
    ReputationRep:
    could somebody explain the following in english? :confused: 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
    Offline

    15
    ReputationRep:
    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...

    Q=a-bp
    bp=a-Q
    p=\frac{a}{b}-\frac{Q}{b}
    • Thread Starter
    Offline

    1
    ReputationRep:
    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)
    Offline

    15
    ReputationRep:
    (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 x instead of x \times 1 .
    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...:o: so I guess you're at uni now? Where are you studying?
    • Thread Starter
    Offline

    1
    ReputationRep:
    lol yeah am at leicester cool will try a separate post for the bertrand competition thing, thanks for all the help!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.