Answer to Question #133315 in Microeconomics for Jennifer

Question

The respective elasticities of demand and supply for a product are -0.55 and 1. Further, it is observed that the price of this commodity is $80 whilst the prevailing quantity in the market is 950. By adopting a demand and supply concept of

Qd = a + bP
Qs = c + dP use the information provided to estimate the values of a,b,c and d.

Answer 1

price elasticity of demand=$\dfrac{\triangle Q^d}{\triangle P}*{P \over Q^d}$

$\Rightarrow -0.55=$ $\dfrac{\triangle Q^d}{\triangle P}*{80 \over 950}$

$\Rightarrow$ $\dfrac{\triangle Q^d}{\triangle P}$ =-0.55*${80 \over 950}$

=-6.53125

$Q^d= a+ bP$

$\Rightarrow$ $\dfrac{\triangle Q^d}{\triangle P}$ $=b$

$\therefore$ $b=-6.53125$

$\Rightarrow Q^d = a+ (-6.53125)p$

taking p =80, Q^d =950

$\Rightarrow 950=a+(-6.51325)(80)$

950 =a-522.5

a=950+522.5

a=1472.5

Q^d =1472.5 -6.51325P

price elasticity of supply $=\dfrac{\triangle Q^s}{\triangle P}*{P \over Q^s}$

$\Rightarrow 1=\dfrac{\triangle Q^d}{\triangle P}*{80 \over 950}$

$\Rightarrow \dfrac{\triangle Q^s}{\triangle P}={950 \over 80}$

=11.875

$Q^s =c +dP$

$\Rightarrow$ $\Rightarrow \dfrac{\triangle Q^s}{\triangle P} =d$

$\therefore$ d=11.875

$Q^s =c +11.875p$

At p =80 , $Q^s =950$

950=c +11.875(80)

950=c+950

c=950-950

c=0

so Q^s =0+11.875p

Q^s =11.875p

$\therefore a=1472.5 , b=-6.53125 , c=0 ,d =11.875$