## Answers

Inverse Demand: P=240-2Q and cost : C(Q) = 40Q

A)

Revenue = Price*Quantity; Revenue = (240-2Q)Q

Marginal Revenue: 240-4Q

The Marginal Cost: MC(Q) =40

**For a monopoly Put: MR=MC and slove for Q**

240-4Q = 40 => **Q* = 50** and the monopolist price would be: P* = 240-2*50 = 140 ; **P*=140**

b)

the dead weight loss: Lets solve for P coordinates and Q values: P=MC ; 240-2Q = 40 => Q=100

Dead Weight Loss= (1/2)(100-50)(140-40)

**Dead Weight Loss= 2500**

c)

For a bertrand competition:

**Bertrand Price would be: P1 = P2 = MC**

as they are both identical so the optimal price they can charge is only MC... so they both do not have any incentive to deviate. As any firm charging more would loose all market.

d)

**There would be Zero Dead Weight Loss in Bertrand equilibrium.**

Under Monopoly P=240-20 DWL = (1/2)(100-50)(140-40) = 2500 140 40 P=MC=40 50 100

Under Bertrand P=240-20 DWL = 0 40 P=MC=40 100

.
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