Market Eqaulibrium
. Eye-de-ho Potatoes is a product of the Coeur d=Alene Growers= Association. Producers in the area are able to switch back and forth between potato and wheat production depending on market conditions. Similarly, consumers tend to regard potatoes and wheat (bread and bakery products) as substitutes. As a result, the demand and supply of Eye-de-ho Potatoes are highly sensitive to changes in both potato and wheat prices.
Demand and supply functions for Eye-de-ho Potatoes are as follows:
QD = -1,450 - 25P + 12.5PW + 0.2Y, (Demand)
QS = -100 + 75P - 25PW - 12.5PL + 10R, (Supply)
where P is the average wholesale price of Eye-de-ho Potatoes ($ per bushel), PW is the average wholesale price of wheat ($ per bushel), Y is income (GNP in $ billions), PL is the average price of unskilled labor ($ per hour), and R is the average annual rainfall (in inches). Both QD and QS are in millions of bushels of potatoes.
A. When quantity is expressed as a function of price, what are the Eye de ho Potatoes demand and supply curves if PW = $4, Y = $7,500 billion, PL = $8, and R = 20 inches?
B. Calculate the surplus or shortage of Eye-de-ho Potatoes when P = $1.50, $2, and $2.50.
C. Calculate the market equilibrium price/output combination.
P3.1 SOLUTION
A. When quantity is expressed as a function of price, the demand curve for Eye de ho Potatoes is:
QD = -1,450 - 25P + 12.5PW + 0.2Y
= -1,450 - 25P + 12.5($4) + 0.2($7,500)
QD = 100 - 25P
When quantity is expressed as a function of price, the supply curve for Eye de ho Potatoes is:
QS = -100 + 75P - 25PW - 12.5PL + 10R
= -100 + 75P - 25($4) - 12.5($8) + 10(20)
QS = -100 + 75P
B. The surplus or shortage can be calculated at each price level:
Price
Quantity
Supplied
Quantity
Demanded
Surplus (+) or
Shortage (-)
(1)
(2)
(3)
(4) = (2) - (3)
$1.50:
QS = -100 + 75($1.50)
= 12.5
QD = 100 - 25($1.50)
= 62.5
-50
$2.00:
QS = -100 + 75($2)
= 50
Demand and supply functions for Eye-de-ho Potatoes are as follows:
QD = -1,450 - 25P + 12.5PW + 0.2Y, (Demand)
QS = -100 + 75P - 25PW - 12.5PL + 10R, (Supply)
where P is the average wholesale price of Eye-de-ho Potatoes ($ per bushel), PW is the average wholesale price of wheat ($ per bushel), Y is income (GNP in $ billions), PL is the average price of unskilled labor ($ per hour), and R is the average annual rainfall (in inches). Both QD and QS are in millions of bushels of potatoes.
A. When quantity is expressed as a function of price, what are the Eye de ho Potatoes demand and supply curves if PW = $4, Y = $7,500 billion, PL = $8, and R = 20 inches?
B. Calculate the surplus or shortage of Eye-de-ho Potatoes when P = $1.50, $2, and $2.50.
C. Calculate the market equilibrium price/output combination.
P3.1 SOLUTION
A. When quantity is expressed as a function of price, the demand curve for Eye de ho Potatoes is:
QD = -1,450 - 25P + 12.5PW + 0.2Y
= -1,450 - 25P + 12.5($4) + 0.2($7,500)
QD = 100 - 25P
When quantity is expressed as a function of price, the supply curve for Eye de ho Potatoes is:
QS = -100 + 75P - 25PW - 12.5PL + 10R
= -100 + 75P - 25($4) - 12.5($8) + 10(20)
QS = -100 + 75P
B. The surplus or shortage can be calculated at each price level:
Price
Quantity
Supplied
Quantity
Demanded
Surplus (+) or
Shortage (-)
(1)
(2)
(3)
(4) = (2) - (3)
$1.50:
QS = -100 + 75($1.50)
= 12.5
QD = 100 - 25($1.50)
= 62.5
-50
$2.00:
QS = -100 + 75($2)
= 50