Question

Consumers will buy 1000 items if the price per item is $35. However, if the price increases by $10, consumers' demand will drop to 750 items. Assuming linear demand, how many items (to the nearest item) will consumers take if the item is free?

(a) 650
(b) 1875
(c) Infinitely many
(d) 75
(e) 150

Answer 1

To determine how many items consumers will take if the item is free, we can use linear demand equation. Using the given data points, the slope of the demand curve can be calculated as -25. By setting the price as $0 in the demand equation, we find that the quantity demanded would be 0.

Step-by-step explanation:

To determine how many items consumers will take if the item is free, we need to understand the relationship between price and quantity demanded. In this case, we are given two data points: when the price per item is $35, consumers will buy 1000 items, and when the price increases by $10, consumers' demand drops to 750 items. Assuming linear demand, we can calculate the slope of the demand curve.

First, we calculate the change in quantity demanded (∆Q) and the change in price (∆P):

∆Q = 750 - 1000 = -250

∆P = 35 + 10 - 35 = 10

Next, we calculate the slope (m) using the formula m = ∆Q / ∆P:

m = -250 / 10 = -25

Finally, we can use the slope-intercept form of a linear equation (y = mx + b) to find the quantity demanded when the price is $0:

0 = -25x + b

Since consumers will not pay anything for the item, the price (x) is 0. Solving for b, we find b = 0.

Therefore, the equation for the demand curve is y = -25x, where y represents the quantity demanded and x represents the price per item. When the price is $0, the quantity demanded would be 0.