Question

Suppose the market for ice cream is characterized by the following:

QD=80-4P

QS=-10+P

A) Do QD and QS obey the laws of demand and supply respectively? How do you know? (5

marks)

B) Solve for the equilibrium price and quantity for ice cream.

C) Rather unexpectedly, a portion of the world’s dairy cows have started to produce sour

milk, which causes the price of milk to increase. Explain how this would affect (ie. shift or

cause movement along) the supply and demand curves. Provide a fully labeled graph of

the effect, showing the old and new equilibrium. What has happened to price and quantity

in the new equilibrium (relative to the old)?

D) With respect to the analysis conducted in part C), if total revenue in the ice cream market

went up when the price of milk increased, what property must be true (with respect to

demand) at the original equilibrium? NOTE: This does not require a

calculation – just explain to me what property associated with the demand curve must

be true at the original equilibrium.

Answer 1

(A)

From demand function, when Price increases (decreases), QD decreases (increases), following an inverse relationship between price and quantity demanded. So it obeys the law of demand.

From supply function, when Price increases (decreases), QS increases (decreases), following a direct relationship between price and quantity supplied . So it obeys the law of supply.

(B)

Setting QD = QS,

80 - 4P = - 10 + P

5P = 90

P = 18

Q = - 10 + 18 = 8

(C)

Increase in price of milk, an input will increase the cost of producing ice cream. So fims will decrease production which will decrease market supply, shifting supply curve leftward. Price will increase and quantity will decrease.

In following graph, D0 and S0 are initial demand and supply curves intersecting at point A with equilibrium price P0 and quantity Q0. After supply increases, S0 shifts left to S1, intersecting S0 at point B with higher price P1 and lower quantity Q1.

(D)

If an increase in price caused by higher cost of inputs causes total revenue to increase, it means that the % Decrease in QD is less than the % Increase in price, meaning demand is inelastic.