Question 6.40: (a) Given the demand function P = 60 − Q², calculate the coe......

(a) P = 60 − Q²

Step 1: Find dQ/dP. Since the demand function is written as P = 60 − Q², find dP/dQ.

$\frac {dP}{dQ} = −2Q$,  then $\frac {dQ}{dP} = \frac {1}{\frac {dP}{dQ}} = \frac {1}{−2Q}$

Step 2: Derive an expression for $ε_d$ in terms of P

= $-\frac {P}{2(60   −   P)}$

Step 3: Evaluate $ε_d$ at P = 44:

= −1.375

Since $ε_d$ < −1, demand is elastic.

(b) Q = $45e^{−0.04P}$

Step 1: Find dQ/dP. Since the demand function is written as Q = $45e^{−0.04P}$,

Step 2: Derive an expression for $ε_d$ in terms of P

Step 3: Evaluate $ε_d$ at P = 10:

This one is easy!

$ε_d$ = −0.04P = −0.04(10) = −0.4

Since $ε_d$ > −1, demand is inelastic.