Question

The demand curve for potatoes is given by:
QX = 1,000 +0.3I - 300 PX + 200 PY,where QX = Annual demand in pounds
I = Average income in dollars per year
PX = price of potatoes per pound,
PY = price of rice per pound.
(a) (1) Discuss whether potato is a normal good or an inferior good.
(b) (1) Suppose I = $10,000: What would be market demand for potatoes?
(1) Determine whether X and Y are substitutes or complements.
(c) (2) The supply curve of product X is given by: Qx = 200 PX – 1000. Determine the equilibrium price and sales of potatoes. Let PY =$25.

Answer 1

(a) Since the coefficient on I =0.3 in the demand for potatoes which means that if income increase by one unit, then demand for potato increases by 0.3 units. So potato is a normal good.

(b) I=$10000

So Qx=4000-300Px+200Py

X and Y are substitutes since in the demand function of X, the coefficient of Py is positive which means that if price of Y increases then demand for X increases.

(c) Supply of X: Qx=200Px-1000

Py=25 So demand for X becomes Qx=9000-300Px

For Equilibrium demand=supply

200Px-1000=9000-300Px

Solving for Px we get the equilibrium price Px=10000/500=20

Equilibrium Quantity=3000