Question

Two points (p, q) on a linear supply function are ($2.55, 98,000) and ($6, 195,500).

⦁ Determine the supply function q = f(p).
⦁ What price would result in supplier offering 145,000 units for sale?
⦁ Interpret the slope of the function.
⦁ Determine the p intercept.
⦁ Sketch f(p)

Answer 1

• q ≈ 28270p +25935
• $4.21 will give a supply of 145,000
• slope is the supply increase per dollar of price
• p-intercept is about -$0.92
• a graph is attached

Explanation:

The two-point form of the equation of a line is useful for this.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

q = (195500 -98000)/(6.00 -2.55)(p -2.55) +98000

q = 97500/3.45(p -2.55) +98000

q ≈ 28269.9p +25934.8

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For a supply of 145000, the price would need to be ...

145000 = 28269.9p +25934.8

119065 = 28270p

119065/28270 = p = 4.21

A price of $4.21 will result in a supply of $145,000.

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The slope is the additional amount supplied for each dollar increase in price.

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The price value that results in a supply of zero is ...

0 = 28270p +25935

-25935 = 28270p

-25935/28270 = p ≈ -0.92

The p-intercept is about -$0.92.