Question

Assume the supply function of ice cream is written as: Qs = 100 + 20P - 5Pm, where Qs is the quantity supplied, P is the price of ice cream, and Pm is the price of milk ($/gallon). When the milk price is $10, the quantity supplied is 100. Suppose milk price decreased by 20% due to the policy change, how will the Qs change?

Answer 1

The Qs will increase by 460 units which also represents a 460% increase in Qs.

Step-by-step explanation:

Step 1: Calculation of price of ice cream, P, when price is $10 and the quantity supplied is 100.

Given:

Qs = 100 + 20P - 5Pm ……………….. (1)

Where:

Qs = 100

P = ?

Pm = $10, or 10

Substituting the values into equation (1) and solve for P, we have:

100 = 100 + 20P - (5 * 10)

100 = 100 + 20P - 50

100 - 100 + 50 = 20P

50 = 20P

P = 50 / 2 = 2.50

Step 2: Calculation of new Qs, Qs1, when milk price, Pm, decreased by 20%.

This implies that we have:

Qs1 = ?

P = 2.50

Pm = $10 * (100% - Percentage decrease in Pm) = $10 * (100% - 20%) = $8, or 8

Substituting the values into equation (1) in Step 1 above and Qs1 for Qs to calculate Qs1, we have:

Qs1 = 100 + (20 * 2.50) - (5 * 8)

Qs1 = 100 + 50 - 40

Qs1 = 110

Step 3: Calculation of change in the Qs when milk price, Pm, decreased by 20%.

Change in Qs expressed in unit = Qs1 - Qs = 110 - 100 = 10

Change in Qs expressed in percentage = ((Qs1 - Qs) / Qs) * 100 = ((110 - 100) / 100) * 100 = 10%

Therefore, the Qs will increase by 10 units which also represents a 10% increase in Qs.