The local lemon market has the following supply and demand relationships:
QD = 100 - 5p - po + 2I
QS = 4p
where p is the price of lemons (per pound), Q is the quantity of lemons in pounds, I is the average consumer income, and po is the price per pound of oranges. Derive the equilibrium price and quantity of lemons as functions of the price of oranges and average consumer income. Use the calculus method of comparative statics to compute the effects of income and the price of oranges on the equilibrium price and quantity of lemons.
Find equilibrium price by setting supply and demand equal:
100 - 5p - po + 2I = 4p
Solving for p:
p = 11.11 - .11po + .22I
To find Q, plug the equilibrium price into either supply or demand:
Q = 44.44 - .44po + .89I
The comparative statics w.r.t. the price of oranges are:
∂p/∂po = -.11
∂Q/∂po = -.44
The comparative statics with respect to income are:
∂p/∂I = .22
∂Q/∂I = .89
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