Question

1. [10 pts] Assume that the market demand and supply curves for soybeans grown in Canada

can be represented via the following:

Q_D = 40 − 0.5P_s. Q_s = 2.5 + 2.5P_s

where PS is the soybean price ($/bushel) and QS is the quantity of soybeans produced (denominated

in 100 million bushel units).

(a) [10 pts] What is the equilibrium price, P*_s, and quantity, Q*_s, of soybeans?

Answer 1

Market equilibrium is the market situation where quantity demanded is equal to quantity supplied. (QD = QS) The corresponding price and quantity at market equilibrium is called equilibrium price and equilibrium quantity.

At market equilibrium, QD = QS

(Equating the given QD and QS to find equilibrium price and quantity)

40 − 0.5Ps= 2.5 + 2.5Ps

40 – 2.5 = 2.5Ps + 0.5Ps

37.5 = 3Ps

Ps = 37.5/3 = 12.5

Equilibrium price of soybean (Ps) = $12.5

Qs = 2.5 + 2.5Ps

(Substitute P = 12.5 to find equilibrium quantity)

Qs = 2.5 + (2.5 * 12.5)

Qs = 2.5 + 31.25

Qs = 33.75

Equilibrium quantity of soybean (Qs) = 33.75 (in 100 million-bushel units)