Question

A company produces two competing products whose demand schedules are
q1 = 219 - 1.8p1 + 0.5p2
q2 = 303 - 2.1p2 + 0.8p1
What price should it charge in the two markets to maximize total sales revenue?

Answer 1

$TR=TR1+TR2=p1q1+p2q2;$

$p1×(219-1.8p1+0.5p2)+p2×(303-2.1p2+0.8p1);$

$=219p1-1.8p1^2+0.5p1p2+303p2-2.1p2^2+0.8p1p2;$

$1.3p1p2+219p1+303p2-1.8p1^2-2.1p2^2;$

$\frac {dTR}{dp1}=219-3.6p1+1.3p2;$

$\frac {dTR}{dp2}=303-4.2p2+1.3p1;$

Multiplying by 42

$9 198 - 151.2p1+54.6p2=0$;

Multiplying by 13

$3939+16.9p1-54.6p2=0;$

$13137-134.3p1=0;$

p$1=98;$

$303-2.1p2+0.8×98; 2.1p2=303+78.4; 2.1p2=381.4; p2= 182;$

Answer : p1= $98 and p2= $ 182.