A monopolist faces a demand curve P = 70 - 1Q, with marginal revenue MR = 70 - 2Q, and MC = 20. Price is expressed in dollars.?

a)How to graph the three functions on one diagram.
b) How to compute the profit-maximizing output and price combination on the graph.
c) How to compute the efficient level of output (where MC = demand) on the graph
d) How to compute the deadweight loss associated with producing the profit-maximizing output rather than the efficient output ?

1 Answer
Nallasivam V
Dec 5, 2016

Profit maximising quantity and price combination.
Price =$.45
Quantity =25 units
DWL =$312.5

Explanation:

Given -

p=70 - Q------ -----------[Demand function]
MR=70-2Q---------------[Marginal Revenue function]
MC=20--------------------[Marginal Cost function]

Diagram

Profit Maximising Price and Output combination

Condition for maximum profit

MR = MC

70-2Q=20
-2Q=20-70=-50
Q=(-50)/(-2)=25
Profit maximising quantity =25 units

Substitute Q=25 in demand function to find the price

p=70-Q
p=70-25=45

Profit maximising price =$45

Condition for Efficient level of output

D= MC
70-Q=20
-Q=20-70=50
Q=50

Efficient level of output =50 units

Dead Weight Loss is the green colour area.

DWL =(25 xx 25)/2=312.5 ----- [Area of the green shaded area - height of the triangle is 25 and base of the triangle is 25]
DWL =$312.5

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