This question drags on quite a bit. Can someone please help me solve it?

Question

Demand for a good is given by Qd=500-30P1+20P2+5I, and P1=2, P2=2, and I=100. P is price, q is quantity, and I is income. Calculate the quantity demanded. Is this a normal good? Is good 2 a substitute or compliment? How to calculate the elasticity of demand if P1 changes to 3, while P2 and I are unchanged? If P1 is unchanged at 2, and I remains at 100, but P2 changes to P2=3. What is the cross elasticity of demand? Finally, P1=2, P2=2, but I rises from 100 to 200. What is the income elasticity?

Answer 1

I tried to make a video on this, but it went way over the video length limit. Here, this should get you started:

To find Qd, just plug in those values into the demand function like so:

Qd = 500 - 30(2) + 20(2) +5(100) = 980

This product is a normal good because as income rises, the quantity demanded rises. Further, the coefficient on income is positive.

Good 1 and Good 2 are substitutes because as P2 rises, Qd1 rises also. You can also tell by looking at the positive coefficient on P2. If the number is negative, then the two products are complements.

To solve for price elasticity of demand, find the % change in quantity and divide it by the percent change in price.

To solve for cross price elasticity, find the % change in quantity and divide it by the percent change in P2.

To solve for income elasticity, find the % change in quantity and divide it by the percent change in income.