Problem 1: Equilibrium price and quantity
Q = 110 - 20p (demand) Q = -10 + 10p (supply)
Equilibrium just means the quantity demanded equals the quantity supplied at the same price.
So set them equal to each other:
110 - 20p = -10 + 10p
Now solve for p, same as any algebra equation:
110 + 10 = 20p + 10p 120 = 30p p = 4
That's the equilibrium price. Now plug p = 4 back into either equation to get Q. I'll use both, just
to check they match:
Demand: Q = 110 - 20(4) = 110 - 80 = 30 Supply: Q = -10 + 10(4) = -10 + 40 = 30
Both give Q = 30, so that confirms it.
Equilibrium: p = 4, Q = 30
Problem 2: Avocado supply shift
Q = 58 + 15p - 5pf
pf is the price of fertilizer. Fertilizer is an input, so it sits in the supply function, not demand,
same way sugar price sat in the coffee demand function as ps.
The coefficient on pf is -5. That number tells you exactly how much Q changes for every $1
change in pf, holding p constant. This is the same idea as ∂Q/∂Y = 0.1 in the coffee example,
just here it's ∂Q/∂pf = -5.
Fertilizer price rises by $1.10, so:
ΔQ = -5 × 1.10 = -5.5
The supply curve shifts left by 5.5 units. Negative because fertilizer is a cost. When a cost
goes up, farmers are willing to supply less at every price, so the whole curve moves left, not just
one point on it.
Problem 3: Supply shift from Pb
Q = 100 + 2Pa - Pb + Pc/3
Same move. Find the coefficient attached to the variable that's changing. Pb has a coefficient of
-1 sitting in front of it.
Pb falls by $4, so:
ΔQ = -1 × (-4) = +4
The supply curve shifts right by 4 units. Makes sense too, Pb dropping by $4 combined with
a negative coefficient flips the sign, so quantity supplied goes up at every price.