Answer to Question #99957 in Macroeconomics for Nathan

Question

Suppose a monopolist faces a demand curve given by P=100-2Q and a total cost curve given by TC=500+20Q
Derive equations for MR MC ATC and graph along with the demand curve

Answer 1

Demand [P]=100-2Q

Total Cost[TC]=500+20Q

Average Revenue [AR}=100-2Q

Total Revenue [TR]=(Q)*(AR)=100Q-2Q²

Marginal Revenue[MR]=d(TR)/dQ=100-4Q

Average Cost[AC]=[TC/Q]=500/Q+20

Marginal Cost[MC]=d(TC)/dQ=20

Set marginal revenue[MR] equal to marginal cost[MC]

100-4Q=20

100-20=4Q

80=4Q

Q=20 units

Plug the monopolist's quantity of output into the demand equation to calculate price.

Demand [P]=100-2Q=100-2x20=$60

Total Cost[TC]=500+20Q=500+20x20=900

Average Revenue [AR}=100-2Q=100-2x20=60

Marginal Revenue[MR]=d(TR)/dQ=100-4Q=100-4x20=20

Average Cost[AC]=[TC/Q]=500/Q+20=500/20+20=45

Marginal Cost[MC]=d(TC)/dQ=20