Question

Q4.   Find equilibrium Price and Quantity and Price Elasticity of Demand from the following demand and supply functions

         i.       Q=10-2P²                      Q=5+3P

         ii.      Qd= 200-40P                Qs= -40+80P

Answer 1

i) $10-2p^{2} =5+3p$

$2p^2+3p-5=0$

$p=1, Q=8$

Price Elasticity of Demand;

$=\frac {d_Q} {d_p} ×\frac {P} {Q}$

Differentiating the demand equation we get ;

$=-4×\frac {1} {8}=-0.5$

ii) $200-40P=-40+80P$

$120P=240$

$P=2,Q=120$

Price Elasticity of Demand;we differentiate the demand equation

$\frac {d_Q} {d_P} =-40$

$=-40×\frac {2} {120}$

$=-0.6667$