Question

Suppose you know that, at a price of $6, the quantity supplied is 25 million pounds, and at a price of $2, the quantity supplied is 15 million pounds. What is the quantity supplied when price is at $8?

Old quantity demanded New quantity demanded Price 10 15 Price per pound 0 5 10 15 20 25 30 35 40 45 Quantity (millions of pounds per month)

Answer 1

We have been given the following information about the quantity supplied and the prices:

Quantity supplied = 25 million pounds when price = $6

Quantity supplied = 15 million pounds when price = $2

Or in other terms, we have been given two data points of a supply curve i.e.

(x1,y1) = (q1, p1) = (25,6)
and
(x2, y2) = (q2, p2) = (15,2)

Let's try to derive the equation for the supply curve

Equation of a line passing through two data points (x1,y1) and (x2,y2) is given as:

(y - y1) = m (x - x1)
where m = (y2-y1) / (x2-x1)

or m = (2-6)/ (15-25) = 4/21

or y - 6 = 4/21 (x - 25)

or 21y - 126 = 4x - 525

or 4x - 21y = 399

Thus, equation of supply curve is 4x - 21y = 399

or converting x and y to prices and quantity,

4q - 21p = 399

Thus, for the new prices = $8, we can easily calculate the quantity supplied using the equation of supply curve.

4q - 21p = 399

or 4q - 21*8 = 399
4q = 231

or q = 231/4 = 57.75 (or Approx 58 units)