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
Dec 5, 2016

Answer:

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#