Suppose there are only two goods – Food (F) and Shelter (S). The demand equations for these two goods depend on their prices, pF and pS as follows:

Question

DF (pF, pS) = 10 – 2pF – pS
DS (pF, pS) = 10 – pF – 2pS
The supply curves depend only on their own prices:
SF (pF) = pF
SS (pS) = 5pS
Determine the equilibrium price and quantity of these goods.

Answer 1

The two equations describing the equilibrium in each market are given by:
pF = 10 – 2pF – pS
5pS = 10 – pF – 2pS
Using the first equation, we can solve for pS in terms of pF:
pS = 10 – 3pF
Substituting this into the second equilibrium condition for pS yields:
7(10 – 3pF) = 10 – pF
Solving for pF = 3.0. Then pS =1.0. The quantities are QF = 3 and QS = 5. Notice that while the demand equations are symmetrical, the higher supply of Shelter results in a lower price and higher quantity in equilibrium.