Question

In: Economics

A monopolist faces a single market with the following demand curve and total cost P =...

A monopolist faces a single market with the following demand curve and total cost

P = 180 – 2.5Q and TC = 2Q2

i. Determine the quantity of output that it should produce and the price it should charge to maximize profit. Then, calculate the profit.

Solutions

Expert Solution

A monopoly produces at MR=MC

P=180-2.5Q

MR=180-5Q .......... An MR curve is double sloped than a linear inverse demand curve

MC is a change in the total cost and a change in function found by differentiation

MC=dTC/dQ=4Q ................ differentiating by power rule.

equating MC=MR

4Q=180-5Q

9Q=180

Q=20

P=180-2.5*20

P=130

the quantity it produces is 20 units and it charges P=$130

==============

Profit=TR-TC

TR=P*Q=130*20=$2600

TC=2*20^2=800

Profit=2600-800

=$1800

the total profit is $1800

Rahul Sunny answered 2 years ago
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