Hi! So I have a question regarding cross-price elasticity and income elasticity , specifically my textbook example which I don't quite understand. Once I have the correct values it is very easy to calculate but this thing has been bothering me. So In the example the demand function is Q = 104 - 40p + 20 pt + 0.01Y. At equilibrium Q = 80 and Y = 4000.

Formula: delta Q/delta Pt * Pt/Q. The textbook example then continues and writes that formula then 20 * Pt/Q(cross price) and 0.01 * Y/Q (income elasticity).

In the example of income elasticity:

Q1 = 104 - 40p + 20 pt + 0.01Y

Q2 = 104 - 40p + 20 pt + 0.01Y

delta Q = Q2 - Q1 = 0.01(Y2-Y1) = 0.01(delta Y). So deltaQ/deltaY = 0.01. THIS I dont understand.

My question is how does delta Q/ delta Y = 0.01? It is just the coefficient infront of Y. The same demand function was used when explaining cross price elasticity where delta Q/ delta Pt = 20, again just the coefficient in front of Pt. Is it safe to always assume that delta Q/delta Pt or whatever equals the coefficient in front of Pt or Y, Pg etc (with regards to what is being calculated). For instance if I wanna calculate income elasticity I just go "yeah deltaQ/deltaY = 0.01". Thanks in advance!