Answer to Question #82302 in Microeconomics for Sarpong Elijah

Question

The demand and supply functions of beans are respectively given as 20QB +15PB-5PR=6000 and 10QB-15PB=1200. Similarly, the demand and supply of rice are QR+PR-PB=250 and 3QR-7PR=710. PB and PR are prices of beans and rice. QB is demand of beans and QR is demand of rice. Find the equilibrium price and quantity of beans and rice. A rice and beans substitute? Explain your answer.

Answer 1

The demand and supply functions of beans are: 20QB +15PB-5PR=6000 and 10QB-15PB=1200.

The demand and supply of rice are: QR+PR-PB=250 and 3QR-7PR=710.

The equilibrium price and quantity of beans are:

Qd = Qs,

6000 - 15PB + 5PR = 2400 + 30PB,

45PB - 5PR = 3600,

PB = 80 + 1/9PR,

QB = (1200 + 15*(80 + 1/9PR))/10 = 240 + 1/6PR.

The equilibrium price and quantity of rice are:

Qd = Qs,

750 - 3PR + 3PB = 710 + 7PR,

PR = 40 + 0.3PB,

QR = 250 - 40 - 0.3PB + PB = 210 + 0.7PB.

A rice and beans are substitutes, because the increase in price of one of the goods will cause the increase in quantity demanded of another good.