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    Determining long run and short run equilibrium

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    Q5. Ten competitive widget makers each have the following cost structure:
    Ci = 0.005qi2 + 4qi + 200 i = 1, 2,....,10
    (a) What is the short-run supply curve for each firm?
    (b) What is the industry supply curve?
    (c) If market demand is:
    Q = 6,500 - 500p
    What are short-run equilibrium market price and quantity?
    (d) At the price determined in (c), is the firm breaking even, making profits or losses?
    (e) In the long-run, firms enter the industry -assume constant costs over long-run-what will be market price and quantity?
    (f) How many firms will there be in the industry?

    © BrainMass Inc. brainmass.com December 24, 2021, 7:43 pm ad1c9bdddf
    https://brainmass.com/economics/supply-and-demand/determining-long-run-short-run-equilibrium-212692

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    Solution:

    (a) What is the short-run supply curve for each firm?

    Ci = 0.005qi^2 + 4qi + 200
    Marginal cost of each firm = MCi=dCi/dqi=0.01qi+4
    In equilibrium MC = Price =p
    pi = 0.01qi+4
    0.01qi=-4+p
    qi= -400+100p

    (b) What is the industry supply curve?
    There are ten firms in market
    Total supply will be Qs=10*qi=(-400+100p)*10
    Qs =-4000+1000p

    (c) If market demand is:
    Q = 6,500 - 500p
    What are short-run equilibrium market price and quantity?

    For equilibrium Qd=Qs
    6500-500p=-4000+1000p
    10500=1500p
    p=7

    Qd=6500-500*7=3000
    Qs=-4000+1000*7=3000
    Equilibrium Price =7
    Equilibrium Quantity = 3000

    (d) At the price determined in (c), is the firm breaking even, making profits or losses?

    At equilibrium, output of each firm =-400+100*7=300
    Total cost of each firm= 0.005qi^2 + 4qi + 200=0.005*300^2+4*300+200=1850
    Total Revenue = output*price=300*7=2100
    Total Revenue > Total cost, firms are making profit in short run.
    Profit of each firm = 2100-1850=250

    (e) In the long-run, firms enter the industry -assume constant costs over long-run-what will be market price and quantity?

    Ci = 0.005qi^2 + 4qi + 200
    Average Cost = TC/q = 0.005qi+4+(200/qi)
    We will find minimum of average cost
    d(ATC)/dq=0.005-200/qi^2
    Put d(ATC)/dq=0
    0.005 -(200/qi^2)=0
    0.005=200/qi^2
    qi^2=200/0.005=40000
    qi=200

    Minimum Average Total Cost = 0.005*200+4+(200/200)=6

    Output of each firm = 200
    Price = Minimum ATC =6
    Quantity demanded = 6,500 - 500p=6500-500*6=3500

    (f) How many firms will there be in the industry?

    Number of firms = Total Demand/ output of each firm = 3500/200=17.5
    There will be 18 firms.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:43 pm ad1c9bdddf>
    https://brainmass.com/economics/supply-and-demand/determining-long-run-short-run-equilibrium-212692

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