Question

1. Deadweight loss of monopoly Suppose that electricity consumers have an inverse demand curve given by: P(C)=1-, There is one supplier of electricity, which has a total cost function given by: ce) = You can assume that there are no externalities associated with electricity consumption or production. 1.1. What is the marginal cost function? Draw the marginal cost function and the inverse demand curve on the same diagram, labeling axes and intercepts. 1.2. What is the socially optimal level of production? Show this point on your diagram from 1.1. 1.3. How much electricity does the monopolist produce, assuming the monopolist maximizes profits? Show this point on your diagram from 1.1. 1.4. Calculate social welfare in 1.1 and 1.2. What is deadweight loss of monopoly?

Deadweight Loss of Monopoly Question: Please provide work to help me understand, thanks!

Answer 1

17 P(e) = 1-2e - demand caree I cle) = 1/4e2 MC = dcle) = YuX2e = e. PA MC p=1-2e Tebal revenue curve, pe = e-%e2 we MR = d(e) de of tur 2 e = 1-1/₂x20 1.2) Socially ceptimal level of out put is at A when demand curce cubs Marginal cast curve. So, at A, the-1-e en e-le [pleja MCT 1-2e = le an he+2e = 1 an ez at l=1, P= 1-2 = 12 1.3) Manapalist maximize profit when I MD=MC occuy le at B . o At B - e=ye on /ete = 1 om 32e - 1 ce = % At e=%, p = 1- " دراما wa 11

1.4 Social welfare - Consumer suphus + prod = AEDA + AOAD semplis 2 % X 1X (1-2) + 2X1 X (2-0) = ² x ² + y ₂ X / and dead weight loss for monopoly = ACBA I at e=², MR = 1-2/ So, ACBA = %* ( 3 3 - 1 3 ) x (1 - 2 / 3 ) = 1/X 1/2 X 1 - 3 To 1 X