Question

The market for barley is characterized by the demand ???(??,??)=200−3??+??QBD(PB,PW)=200−3PB+PW and supply ???(??,??)=??QBS(PB,PW)=PB, whereas the market for wheat is characterized by ???(??,??)=400−3??+2??QWD(PW,PB)=400−3PW+2PB and ???(??,??)=??QWS(PW,PB)=PW where quantities are in tons. ??PB is the price per tons of barley and ??PW is the price per tons of wheat.

a) (2) Say whether barley and wheat are substitutes or complement? Is that through consumption or production?

b) (4) Find the general equilibrium in the barley and wheat markets.

c) (4) Suppose the demand for barley suddenly increases by 300 tons. What is the new general equilibrium?

Answer 1

a) They are substitutes because d(QDB)/d(PW) = 1 > 0 which means that as PW increases, QDW will decrease but QDB will increase which means that they are substitutes.
It is thriugh consumption.

b) At equilibrium, QDB = QSB and QDW = QSW
When QDB = QSB, we get,
200 - 3PB + PW = PB
So, 3PB + PB = 4PB = 200 + PW
So, PB = (200/4) + (PW/4)
So, PB = 50 + 0.25PW

When QDW = QSW, we get,
400−3PW+2PB = PW
So, 400 + 2(50 + 0.25PW) = PW + 3PW = 4PW
So, 400 + 100 + 0.5PW = 4PW
So, 4PW - 0.5PW = 3.5PW = 500
So, PW = 500/3.5
So, PW = 142.86

PB = 50 + 0.25PW = 50 + 0.25(142.86) = 50 + 35.715
So, PB = 85.72

QB = QSB = PB = 85.72

QW = QSW = PW = 142.86

c) New QDB = 200 - 3PB + PW + 300 = 500 - 3PB + PW

When QDB = QSB, we get,
500 - 3PB + PW = PB
So, 3PB + PB = 4PB = 500 + PW
So, PB = (500/4) + (PW/4)
So, PB = 125 + 0.25PW

When QDW = QSW, we get,
400−3PW+2PB = PW
So, 400 + 2(125 + 0.25PW) = PW + 3PW = 4PW
So, 400 + 250 + 0.5PW = 4PW
So, 4PW - 0.5PW = 3.5PW = 650
So, PW = 650/3.5
So, PW = 185.71

PB = 125 + 0.25PW = 125 + 0.25(185.71) = 125 + 46.4275
So, PB = 171.43

QB = QSB = PB = 171.43

QW = QSW = PW = 185.71