Price Determination Under Perfect Competition. This article explain how industry and firms determine price in long and short runFull description
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dealing with competition
Descripción: 'Perfect' from Edges: A Song Cycle by Pasek & Paul
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Método desarrollado por el Dr. Andrei Shleifer para tarificar los precios en monopolios (1985). Muy utilizado actualmente por los Organismos reguladores de servicios públicos.Descripción completa
Below is a numerical exercise about perfect competition. It may be really useful to solve it before answering questions 6 - 8 in the quiz. You can try first by yourself an then chec! your answers with the solution given at the en.
In the toothbrush inustry aggregate eman is given by" by " # $ 8%%% & '() *here is a number of ientical+ perfectly competitive firms active in the inustry+ with the following costs of prouction" , $ 6 / $ ( 0 1q 23 $ ( 0 q
a. 4uppose 4uppose each firm firm is able to to sell as many many toothbrus toothbrushes hes as it wants wants at the the price of of 1%. 5ow many toothbrushes will each firm prouce
b. 5ow many firms are currently active in the inustry 7hat is the short run inustry supply curve
c. 7hat is the typical typical firm firmss economic economic profit9l profit9loss oss 7hat 7hat o you thin! thin! will will happen happen to the number of firms in this inustry in the long run
. 7hat is is the long long run equilibri equilibrium um price+ price+ )+ )+ an quantitie quantitiess q+ #. 5ow many active firms+ :+ will there be in the long run
ANSWER KEY
a. 4uppose each firm is able to sell as many toothbrushes as it wants at the price of 1%;. 5ow many toothbrushes will each firm prouce
7e !now that the profit maximizing quantity is where / $ /<. 4ince we are in perfect competition+ ) $ /< so / $ ). *herefore+ we can use the / equation to fin the quantity q each firm will prouce. MC = P
⇒
(+ 1q = 1%
⇒
q=
'6 1
= 8
b. 5ow many firms are currently active in the inustry 7hat is the short run inustry supply curve
*he aggregate supply quantity #s is equal to the quantity prouce by each firm q multiplie by the number of firms : in the mar!et" Q s = N ∗q
⇒ N =
Q s
.
q
In orer for the mar!et to be in equilibrium+ the quantity emane must be equal to the quantity supplie" Q s = Q d . *o get the quantity emane in the mar!et we =ust nee to substitute ) $ 1% in the eman curve given by the exercise" Q d = 8%%%− '() = 8%%% −'(∗1% = 8%%% − 18% = 7720
5ence+ Q s = Q d = >>1%
an N =
Q s q
=
>>1% 8
= 965
.
7e have the supply curve by each iniviual firm+ which is MC = P = (+ 1q but we still nee to fin the short run inustry supply curve. ?oing bac! to the equation for the aggregate supply quantity #s + we get
q=
Q s N
=
Q s @6A
.
If we substitute the above equation for q into the iniviual supply curve we fin the short run inustry supply curve P = ( + 1q = (+
1# s @6A
⇒ Qs
482.5P
1,90
c. 7hat is the typical firms economic profit9loss 7hat o you thin! will happen to the number of firms in this inustry in the long run
*he economic profit is equal to total revenues minus total cost. TR = P ∗q = 1%∗8 = '6% TC = TVC + FC = AVC ∗q+ FC = ( (+ q ) q+ 6 = '1∗8+ 6 = '1 Π = TR − TC =
'6%− '.1 = 28
2s you can see+ there are positive profits in the toothbrush inustry so we expect : to increase because new firms will enter the mar!et in the long run.
. 7hat is the long run equilibrium price+ )+ an quantities q+ #. 5ow many active firms+ :+ will there be in the long run
*his is the tric!iest part. In orer to fin the equilibrium price )+ we nee to use two conitions"
– the profit maximization conition ) $ / – the long run zero-profit conition ) $ 2*. By combining the two+ we get / $ 2*. *he exercise oesnCt give us the irect formula for 2* but we can easily erive it from the 23 an ,. ATC = AVC + AFC = AVC +
.6 FC . = ( + q+ q q
4o+ equating / an 2*+ we get" MC = ATC
⇒
( + 1q = ( + q +
.6 q
⇒
q
1
=
.6
⇒
q
=6
.
By substituting q $ 6 in the iniviual supply curve+ we fin the price )" P = MC = (+ 1q = (+ 1∗6 = 16
*he eman curve is the same as in the short run so" Q d = 8%%%− '() = 8%%% −'(∗'6 = 8%%%− 11( = 7776
2gain+ we can compute the number of firms active in the mar!et in the long run in the same way we i for the short run" Q s = Q d = >>>6
an N =
Q s q
=
>>>6 6
= 1296
.
2s expecte+ the number of firms : has increase because new firms have entere the mar!et+ attracte by the positive economic profits. ,inally+ we can write the aggregate supply curve" q=
Q s N
=
Q s '1@6
P = MC = ( + 1q = ( +
⇒
1# s '1@6
⇒
Qs
648P
7hat about profits 7e are in a long run equilibrium so the zero-profit conition hols" P = ATC