Answer to Question #171614 in Microeconomics for Andrew

Question #171614

Consider an electricity market where there are three suppliers, each with constant marginal cost (a reasonable approximation in electricity generation). Firm 1 has a capacity of 200 at MC = 5. Firm 2 has a capacity of 100 at MC = 8. Firm 3 has a capacity of 100 at MC = 10.

  1. Ifthethreefirmsarepricetakers(i.e.,behavecompetitively),whatistheindustrysupplycurve?
  2. ComputetheequilibriumpriceandquantitywhenthemarketdemandisQ(P)=1000/P0.5.
  3. Compute the equilibrium price and quantity when the market demand is Q(P) = 750/P0.5.
  4. ComputetheequilibriumpriceandquantitywhenthemarketdemandisQ(P)=500/P0.5.
1
Expert's answer
2021-03-18T00:19:49-0400

1) For the first firm we have the supply curve Qs1=40P,Q_{s1}=40P, for the second firm - Qs2=12.5PQ_{s2}=12.5P and for the third one - Qs3=10P.Q_{s3}=10P. Then, we can find the industry supply curve:


Qs=Qs1+Qs2+Qs3,Q_s=Q_{s1}+Q_{s2}+Q_{s3},Qs=40P+12.5P+10P=52.5P.Q_s=40P+12.5P+10P=52.5P.

2) Market equilibrium occurs when Qp=QsQ_p=Q_s:


1000P=52.5P,\dfrac{1000}{\sqrt{P}}=52.5P,106P=2756.25P2,\dfrac{10^6}{P}=2756.25P^2,P=1062756.253=$7.13.P=\sqrt[3]{\dfrac{10^6}{2756.25}}=\$7.13.Q=1000$7.13=374.5.Q=\dfrac{1000}{\sqrt{\$7.13}}=374.5.

3)

750P=52.5P,\dfrac{750}{\sqrt{P}}=52.5P,562500P=2756.25P2,\dfrac{562500}{P}=2756.25P^2,P=5625002756.253=$5.89.P=\sqrt[3]{\dfrac{562500}{2756.25}}=\$5.89.Q=750$5.89=309.Q=\dfrac{750}{\sqrt{\$5.89}}=309.

4)

500P=52.5P,\dfrac{500}{\sqrt{P}}=52.5P,250000P=2756.25P2,\dfrac{250000}{P}=2756.25P^2,P=2500002756.253=$4.49.P=\sqrt[3]{\dfrac{250000}{2756.25}}=\$4.49.Q=500$4.49=236.Q=\dfrac{500}{\sqrt{\$4.49}}=236.

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