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Math Help - supply, demand and price equilibrium in perfect competitive market

  1. #1
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    supply, demand and price equilibrium in perfect competitive market

    I'm having trouble to calculate the following problems. if any one can, please help!!!

    " The Market for good X is perfectly competitive. the demand and supply functions of good X are given as follows:
    Qd= 6000 - 30P
    Qs= -500 +20 P

    Where Qd is quantity demanded in thousands units, Qs is quantity supplied in thousands units, and P is the price in dollars for good X. All firms in the market are identical. The market is in long-run equilibrium and there are 1,000 firms producing good X under thsi initial long-run equilibrium.

    a) What are the equilibrium market price and market quantity for good X?
    b) what is the out put of each firm in the initial long-run equilibrium?

    Now suppose the government gives an $8 per-unit subsidy to the consumers for each unit of good X consumed.

    c) after the provision of the per-unit subsidy to the consumers, what are the short-run equilibrium market price and market quantity for good X?
    d) Out of the $8 per-unit subsidy to the consumers, what are the short-run equilibrium market price and market quantity for good X?
    e) What are the long-run equilibrium market price and market quantity for good X?
    f) Out of the $8 per-unit subsidy of good X, how much is the share received by the consumers in the long run?
    g) Explain whether the number of firms in the new long-run equilibrium is larger or smaller than 1,000 and whether the new long-run equilibrium market output is larger or smaller than the initial level. "
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  2. #2
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    Solve Qd = Qs? Surely this will get you started.
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  3. #3
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    Ya.. i got the part a & b, but now, when the government gives an $8 per-unit subsidy, which mean the demand curve will shift right, thus the equilibrium price & demand will increase. but How much??? don't know how to calculate it.. with the given info...

    please help......
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  4. #4
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    What's "P"?

    If the government pays the first $8, isn't that now "P-8" to the consumer?
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  5. #5
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    I don't think it works that way....

    casue government provide subsidy to consumer.. more consumer will demand for the product X .. that there will be increase in demand. if the demand increase the price will go up as well as the supply will go up.....


    increase in both demand & supply & price...
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  6. #6
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    That's what I said.

    Compare

    Unsubsidized

    Qd= 6000 - 30P
    Qs= -500 +20 P

    vs. Subsidized

    Qd= 6000 - 30(P-8)
    Qs= -500 +20 (P-8)
    Attached Thumbnails Attached Thumbnails supply, demand and price equilibrium in perfect competitive market-sdsub.jpg  
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  7. #7
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    Thank You So much TKHunny

    I really appreciate your help.... it's very helpful to me....

    Thank again...

    Khun Aung
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  8. #8
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    Hi,, here is what i got...

    At equilibrium, Qd=Qs
    6000-30P=-500+20P
    P=130
    Therefore

    Qd=6000-30(130)=2100
    Qs=-500+20(130)=2100


    $8 per-unit subsidy to consumers D move to Dí but the supply curve remain unchange


    We need to find the equation of the new demand curve ( Dí)
    now P=138


    Qd =2100= Y-30(138)
    Y=6240


    the equation for new demand cruve is Qd'=6240-30P


    at equalibrium Qd'=Qs


    6240-30Pe=-500+20Pe
    Pe=134.8


    Qd=Qs=Qe=2196*1000= 2,196,000 units


    Plz refer to the graph...
    Attached Thumbnails Attached Thumbnails supply, demand and price equilibrium in perfect competitive market-sd.jpg  
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