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

(2.5,8.5), (3.3,10.5) are two points on the supply curve

the line has slope = (10.5-8.5)/(3.3-2.5) = 2/.8 =5/2

the equation is Q=(2.5)P + b. solve for b by plugging in either point

8.5= (2.5)(2.5) +b

8.5 = 6.25 + b

b= 8.5-6.25 = 2.25

the supply equation is Q=2.5P + 2.25

where Q = quantity supplied measured in millions of bushels, and P=price in dollars per bushel

this is a little strange as at zero price, growers supply 2 1/4 million bushels for free. But it might be realistic as a short run situation,

(2.5, 9.8) and (3.3, 7.8) are two points on the demand curve, The line through them has slope = (9.8-7.8)/(2.5-3.3) = 2/-.8 = - 2.5

the equation of the demand curve is Q=-2.5P+ b

solve for b by plugging in either point

9.8 = -2.5(2.5) + b

b = 9.8+6.25= 16.05

Q=-2.5P + 16.05

For equilibrium P and Q, set the two equations equal to each other

2.5P + 2.25 = -2.5P + 16.05

5P = 16.05-2.25 = 13.80

P = 13.8/5 = $2.76 per bushel

Q = 2.5(2.76)+ 2.25 = 9,150,000 bushels

at $3 a bushel

Qs = 2.5(3) + 2.25 = 7.5 + 2.25 = 9.75 million supplied

Qd = -2.5(3)+ 16.05 = -7.5+16.05 = 8.45 million demanded

There's a surplus at $3, or at any price higher than the equilibrium price of $2.76. At $3 there is a 1.2 million bushel surplus. At $2.50 there is a 1.3 million shortage. At $3.30 there is a 2.7 million surplus

at any price less than $2.76 there is a corn shortage