Question

Industry demand and supply functions for potatoes are as follows:

            Q_D = -1,450 – 25P + 12.5P_W + 0.1Y

            Q_S = -100 + 75P – 25P_W – 12.5P_L + 10R

Where:

Q is number of potato bushels (in millions).

P is the avg. wholesale price of potatoes (in $/bushel).

P_W is avg. wholesale price of wheat (in $/bushel), estimated to be $4.

Y is annual income (GDP in $ billions); estimated to be $15 trillion.

P_L is avg. price of unskilled labor ($/hour); estimated to be $8.

R is avg. annual rainfall (in inches); estimated to be 20 inches.

a) What are the demand and supply curves for potato bushels? (10 points)

b)  Determine if there is a surplus or shortage at P = $1.50 and $2.50 (5 points)

c)   Calculate the equilibrium price/output combination. (5 points)

d)  Do the following events constitute a shift in demand or movement along the demand curve, and in what direction: (5 points)

i. GDP falls by 1%

ii. price rises from $2.00 to $2.50

Answer 1

a) Q_D = -1,450 – 25P + 12.5P_W + 0.1Y = -1,450 – 25P + 12.5(4) + 0.1(15000) = -1450 - 25P + 50 + 1500 = 100 - 25P
(As Y = $15 trillion = $15,000 billion)
So, Q_D = 100 - 25P

Q_S = -100 + 75P – 25P_W – 12.5P_L + 10R = -100 + 75P – 25(4) – 12.5(8) + 10(20) = -100 + 75P - 100 - 100 + 200
So, Q_S = -100 + 75P

b) P = $1.50
QD = 100 - 25(1.5) = 100 - 37.5 = 62.5
QS = -100 + 75(1.5) = -100 + 112.5 = 12.5
So, there is a shortage as demand > supply.

P = $2.50
QD = 100 - 25(2.5) = 100 - 62.5 = 37.5
QS = -100 + 75(2.5) = -100 + 187.5 = 87.5
So, there is a surplus as supply > demand.

c) At equilibrium, QD = QS. So,
100 - 25P = -100 + 75P
So, 75P + 25P = 100 + 100
So, 100P = 200
So, P = 200/100
So, P = 2

Q = 100 - 25P = 100 - 25(2) = 100 - 50 = 50
So, Q = 50

d)
(i) A fall in GDP will cause a leftward shift of the demand curve.
(ii) A rise in price will cause a movement along the demand curve in the upward direction.