ITPEC FE Subject A April 2024 Question 59

Topic: Corporate Activities

When a relation between the list price of a product and the demand for the product is defined as a linear equation, which of the following is the appropriate numerical value to be inserted into blank A below?

(1)When the list price is set to $30, the demand is 0 units.(2)When the list price is set to $10, the demand is 60,000 units.(3)When the list price is set to $15, the demand is A units.

Explanation

45,000 — find the straight line through the two given points, then read it at 15 dollars.

  • •Slope: (60,000 − 0) ÷ (10 − 30) = −3,000 units per dollar
  • •Demand: D = −3,000 × (p − 30) = 90,000 − 3,000p
  • •At p = 15: 90,000 − 45,000 = 45,000 units

Check with proportions: cutting the price from 30 to 15 dollars is 15 ÷ 20 = 3 ÷ 4 of the cut to 10 dollars, so demand is 3 ÷ 4 of 60,000.

Answer (d)

Why not others:

  • •(a) 30,000 — halves 60,000 because 15 is half of 30, as if 60,000 were the demand at price 0 (the line gives 90,000 there); 30,000 is the demand at 20 dollars
  • •(b) 35,000 — lies on the line only at a price of about 18.33 dollars
  • •(c) 40,000 — 60,000 × 10 ÷ 15, treating demand as inversely proportional to price, which is not a linear relation

Key rule: For a linear demand function, take the slope from two known points and substitute the new price; do not assume demand is proportional or inversely proportional to price.

Corporate Activities · AI-written, may contain errors

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