Question

Consider two identical Cournot firms that have zero marginal cost facing the market inverse demand function: P = 100−1/2 Q What is the quantity produced by each firm? Round your answer to the nearest 1 decimal places.

Answer 1

Both firm produced 66.7 output

we have P loor IQ 2 where Q = Q + Q₂ =) P = looo! 100-19.- 12 M(2=0 M Cio have we reaction curue to find for both firm. we reaction get curue by Marginal revenue Marginal cost MR putting MC = firm D To tal revenue = PXQU 100-10-422Q 2 - los@, - +0.000 CS Scanned with CamScanner

2 we get marginal revenue (MR) By differentiating won with Total revelle respect to a MR - 100 2 Qu Iar 2 2 MR, 100 - Q Q1 = 522 Now put MR, - MCA 100 - Q-102 =0 2 loo H100 1 = Q 2 L firm a reaction Cuone Icsl

3 - Similarly firm Total Revenue 2 TR2 = 100 Q2 1oQ IQ 2 2 So MR₂ = loo -2 Q2 to 2 2 MR₂ = 10o IQ - Q2 2 MR = MG 1oo I a Q2-0 2 Too-1 Q - Q2 firm deaction Curre 2 H tuese in firm reaction put Cotue CS Scanned with CamScanner

& Q loo. I Q2 2 O, loo loo I loo 2 2 50 les t I Q 21 50 I QI= o 4 4Q 50 4 30 = 50 x 4 01 200 3 Q = 66. put la = 66.7 in Q2 Q2 loo ♡ 2 CS Scannied with CamScanner

5 |oo | | D ४ 2 22 - 100 -1 (66.1) | 00 - 33.35 30 66.1 3D म P CS Scanned with CamScanner
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