SOLUTION: Retailers will buy 12 cordless phones if the price is $52, and each will buy 16 if the price is $48. The wholesaler will supply 13 phones at $47 each and 15 at $53 each. Assuming t

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Question 1162036: Retailers will buy 12 cordless phones if the price is $52, and each will buy 16 if the price is $48. The wholesaler will supply 13 phones at $47 each and 15 at $53 each. Assuming the supply and demand functions are linear, find the market equilibrium point.
Answer by greenestamps(13216) About Me  (Show Source):
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Let x be the number of phones and y be the price.

Demand: (12,52) and (16,48)

The slope is -1 (a decrease of 4 in the price (y) causes an increase of 4 in the number of phones (x); -4/4 = -1).

Use either point to find the demand equation y+=+-x%2B64

Supply: (13,47) and (15,53)

The slope is 3 (an increase of 6 in the price (y) causes an increase of 2 in the number of phones (x); 6/2 = 3).

Use either point to find the supply equation y+=+3x%2B8

Equilibrium is when the supply and demand are equal:

3x%2B8+=+-x%2B64
4x+=+56
x+=+14

demand: y+=+-14%2B64+=+50
supply: y+=+3%2814%29%2B9+=+50

Market equilibrium is 14 phones at $50 each.