In the market of a monopolistically competition the price of a long-run equilibrium, the consumers’ surplus is equal to a half of fixed cost value, and the price elasticity is equal to the ratio of total to fixed costs.consumer surplus; price elasticity

Grebennikov, Petr I

English

Research Papers in Economics

Petr I. Grebennikov,  
DSc, Professor, Saint-Petersburg University of Economics and Finance. 
 
The theorem of consumer surplus and demand elasticity at 
equilibrium price in a monopolist competition case 
 
Theorem: Let the monopolist competitor production demand has a linear function type, and its 
total production cost is given by formula TC = F + vQ, where F and v stand for fixed and 
average variable costs, and Q is a production quantity. Then, at the price of a long-run 
equilibrium, the consumers’ surplus is equal to a half of fixed cost value, and the price elasticity 
is equal to the ratio of total to fixed costs. 
 
The proof:  
1) In the case of monopolist competition long-run equilibrium, the average cost curve AC = F/Q 
+ v is tangent to the demand curve P = g – hQ (see the figure below). Total consumers’ surplus 
value is presented, then, by the gEP0 triangle area that is equal to 0,5Q0 times the length of the 
leg gP0; the latter being equal to hQ0 product, where h = |dAC/dQ| = F/Q0
2. Finally, one gets 
that the surplus equals to 0,5Q0F/Q0
2Q0 = 0,5F. 
 
2) In the long-run equilibrium, P = AC = F/Q + v, hence giving Q = F/(P – v), and  
    dQ/dP = –F/(P – v)
2. Therefore: 
                
 
 
2
D P P v dQ P F P AC TC
e
dP Q F P v AFC TFC Pv

       
 
. 
 
 
 
 
Q0 
AC 
P 
Q 
D 
P0 
g 
AC 
P 
Q 
D 
g 
E 
 
tg = h 
 
v 
F 
F/2 

The theorem of consumer surplus and demand elasticity at equilibrium price in a monopolist competition case

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics