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23 Jul 2008, 08:39
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The equation for a linear demand function is:
D(p) = 10,000 – 60p
Due to a decline in demand the demand function shifts so that its graph is parallel to the graph of the original function and yields a demand of 2,500 when the price is $100. What is the demand when the price is $80?
Any thoughts? Thanks!
D(p) = 10,000 – 60p
Due to a decline in demand the demand function shifts so that its graph is parallel to the graph of the original function and yields a demand of 2,500 when the price is $100. What is the demand when the price is $80?
Any thoughts? Thanks!
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Updated on: 23 Jul 2008, 09:09
Originally posted by jallenmorris on 23 Jul 2008, 08:43.
Last edited by jallenmorris on 23 Jul 2008, 09:09, edited 1 time in total.
Last edited by jallenmorris on 23 Jul 2008, 09:09, edited 1 time in total.
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3700.
Here is my reasoning. This is in the form of a line equation: y = ax + y where a = slope.
A key is that the new line is going to be parallel to the old one. This tells us that -60 did not change, but the 10,000 did. We have to know this because in the D(p) = 10,000 - 60p we have 2 variables (10,000) and (-60). Changing either one fo them changes the line, but because the new line is parallel, -60 remains constant. If it changed, the new line would not be parallel to the old line formed by the equation.
So, plug in what new info the stems provides:
2500 = x - 60($100)
2500 = x - $6000
+6000 and +6000
$8500 = x
now we have D(p) = 8500 - 60p
we're told to find demand when p = $80
8500 - 60(80) = ?
8500 - 4800 = 3700
Here is my reasoning. This is in the form of a line equation: y = ax + y where a = slope.
A key is that the new line is going to be parallel to the old one. This tells us that -60 did not change, but the 10,000 did. We have to know this because in the D(p) = 10,000 - 60p we have 2 variables (10,000) and (-60). Changing either one fo them changes the line, but because the new line is parallel, -60 remains constant. If it changed, the new line would not be parallel to the old line formed by the equation.
So, plug in what new info the stems provides:
2500 = x - 60($100)
2500 = x - $6000
+6000 and +6000
$8500 = x
now we have D(p) = 8500 - 60p
we're told to find demand when p = $80
8500 - 60(80) = ?
8500 - 4800 = 3700
wc2005
