Elasticity of Demand

[jessi_helt]

Another problem that I can't seem to transfer the application to a particular function. The function reads as followers lnq=D-.47lnp. Where p represents price, D represents a constant for each year, q represents the demand. How do I calculate the elasticity of demand. I know that E= -(p/q)*(dq/dp)

 

[HallsofIvy]

Another problem that I can't seem to transfer the application to a particular function. The function reads as followers lnq=D-.47lnp. Where p represents price, D represents a constant for each year, q represents the demand. How do I calculate the elasticity of demand. I know that E= -(p/q)*(dq/dp)

Do you know what \(\displaystyle \frac{d(ln(q))}{dq}\) and \(\displaystyle \frac{d(ln(p))}{dp}\) are?

Do you know that \(\displaystyle \frac{d(ln(q))}{dp}= \frac{d(ln(q))}{dq}\frac{dq}{dp}\)? (chain rule)

 

[JohnZ]

you can do d(ln(q))/dp = d(ln(q))/dq*(dq/dp) as HallsofIvy said, or you can exponent(?) e to both sides, q=e^(D-0.47*ln(p))=e^D*e^(-0.47*ln(p))=e^D*(e^ln(p))^(-0.47)=
e^D*p^(-0.47)
take a derivative with respect to p
dq/dp=e^D*(-0.47)*p^(-1.47)
so elasticity = 0.47*e^D*p^(-1.47)*p/q
you can simplify it even more.