Question

a) If the supply equation is Q = 7 + 0.1P + 0.004P2 find the price elasticity

of supply if the current price is 80. Is supply elastic, inelastic or unit

elastic at this price? Estimate the percentage change in quantity supplied if

the price rises by 5%.

Answer 1

$Q$ = $7+0.1P+0.004P^2$

if $P=80,$

$Q=40.6$

elasticity Is given by;

= $\frac{change in Q}{change in P×\frac{p}{q}}$

$\frac{change in Q}{change in P}$ is rise over run. It is the

gradient. Q= Y and P = x.

In order to find the gradient, you must differentiate.

$\frac{dQ}{Dp}$ = $0.1+0.008$

Therefore,

$0.1+0.008p×\frac{P}{Q}=elasticity$

$0.1 + 0.008p ×\frac{ 80}{40.6} = 1.458$

b) If the demand equation is $P = (100 - 2Q)$ find the price elasticity of

demand if the current price is 6.

$P = 100 - 2Q$

$2Q = 100- P$

$Q = 50 -\frac{1}{2 }p$

To find change in Q/ change in P, differentiate--- and get $\frac{1}{2}$

=$-0.5×\frac{6}{50-47}$

= $-1$

if price increases by 5 %, given that change in Q/ Change in price = $\frac{-1}{2}$

quantity must decrease by 2.5 %.