At a price of $2.50 per bushel, the annual Canadian supply and demand for corn are 8.5 and 9.8 million bushels, respectively.

Question

At a price of $2.50 per bushel, the annual Canadian supply and demand for corn are 8.5 and 9.8 million bushels, respectively. When the price rises to $3.30, the supply increases to 10.5 million bushels while the demand decreases to 7.8 million bushels.

a) [9 points] Assuming that the supply and demand equations are linear, find the equations for each.

b) [5 points] Find the equilibrium price and equilibrium quantity for the Canadian corn market.

c) [1 point] At a price of $3.00 per bushel, there will be a shortage or surplus of corn in the Canadian corn market?

Answer 1

2.50 price has 8.5 supply and 9.8 demand

actually it should read quantity supplied and quantity demanded at $2.50

(economists and economics instructors get very picky over the distinction between "supply" and "quantity supplied" or between "demand" and "quantity demanded")

point on the supply curve is (8.5, 2.5) and point on the demand curve is (9.8, 2.5)

another point is (10.5 , 3.3) on the supply curve and (7.8, 3.3) on the demand curve

For the supply curve (line), the points are (8.5,2.5) and (10.5, 3.3) They have a line through them with slope = (3.3-2.5)/(10.5-8.5) = .8/2 = .4

the supply line is (y-2.5)/(x-3.3) = .4

y - 2.5 = .4x - 1.3.2

y = .4x - 1.32

for the demand curve (line) the points are (9.8, 2.5) and (7.8, 3.3)

Its slope is (3.3- 2.5)/(7.8-9.8) = .8/-2 = -.4

demand curves have negative slope, supply curves have + slope (with rare exceptions)

demand line is (y-2.5)/(x-9.8) = -.4

y-2.5 = -.4x + 3.9.2

y = -.4x + 9.8

to find equilibrium price set the 2 equations equal and solve for x

-4x + 9.8 = .4x -1.32

.8x = 11.12

x = 11.12/.8 = 1.39

y = 9.8 - 4x = 9.8 - 4(1.39) = 9.8 - 5.56 = 4.24

equilibrium point is (1.39, 4.24) with equilibrium price = 4.24

equilibrium quantity is 1.39

at $3 price is there a shortage or surplus?

3 = 9.8-4x

4x = 6.8

x = 6.8/4 = 1.7 quantity demanded

3 =.4x - 1.32

4x = 4.32

x = 4.32/4 = 1.08 quantity supplied

1.7 > 1.08, so there is a shortage