Price elasticity of demand

[khris le]

This is a picture of an assignment that I have to complete for microeconomics. I am desperate and don't know of where else I can get help.
For the first part of part a, I used simple substitution of the information given into the function.

This is the formula for price elasticity of demand but I don't understand how to use it with the information that was given.


This is my working so far

 

[JeffM]

Do you remember the idea of the slope of a straight line from first year algebra?

Your definition of elasticity is equivalent to $\dfrac{\Delta Q}{\Delta P} \div \dfrac{Q}{P}$. This does not look right to me. Is there no absolute value aspect to how elasticity is defined in your book?

Assuming everything is fixed except the price of good X, what is the function relating price and quantity exchanged?

You calculated the value of that restricted function (restricted because you are assuming everything except the price of good X is fixed). I did not check your arithmetic and have just assumed it is correct. So Q/P = 12/9. When you divide by that, it is the same as multiplying by 9/12.

To calculate $\dfrac{\Delta Q}{\Delta P}$, you need to calculate the slope of the restricted function. You do that by trying a price different from 9. Say you choose 10. Then $\Delta P = 10 - 9 = 1.$ So if the price of good X is 10 what is the quantity demanded if everything else stays the same?