A monopolist incurs marginal cost equal to 2 per unit This p

A monopolist incurs marginal cost equal to $2 per unit. This period, it must pay a $100 fixed cost, and faces demand P(Q)=7- 0.5xQ. What are its profits this period?

Round to two decimal places and do not enter the dollar sign.

Solution

Answer.) Marginal Cost(MC) = $2 and Fixed Cost = $100

Demand P(Q) = 7 - 0.5Q

multiply both sides by Q

TR = 7Q - 0.5Q²

Diff. w.r.t. Q

MR = 7 - 2Q

for equilibrium , MR = MC

7 - 2Q = 2

Q = 2.5

Put value of Q in demand curve  

P = 7 - 0.5(2.5)

P = 7 - 1.25

P = $5.75

Total Cost =( MC×Quantity ) + Fixed Cost = ($2 × 2.5) + 100 = $105

Total Revenue = Price x Quantity = ($5.75 × 2.5 ) = $14.38

Profit = Total Revenue - Total Cost = $14.38 - $105 = -90.62

Negative Profit means Its a loss.