Question

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.

Answer 1

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

$$Q_s=Q_{s1}+Q_{s2}+Q_{s3},$$ $$Q_s=40P+12.5P+10P=52.5P.$$

2) Market equilibrium occurs when $Q_p=Q_s$:

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

3)

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

4)

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