OK.. let me try..
Assume
q = mp + c (i.e. linear function) --- ( i)
for some other value of p and q say, p' and q ' , eqn (i) still holds .. i.e.
q' = mp' + c ------ (ii)
But, if p increases by $5, q drops by 2 item, i.e. for p' = p + 5, q' = q - 2.... with this eqn (ii) becomes,
q - 2 = mp + 5m + c --- (iii)
Subract (i) from (iii)... and you get m = - 2/5 and put this value in eqn (i) to get
q = -2p/5 + c ---- (iv)
Now, your task is to find the value of constant c.
But question says, would buy 100 itmes if price is $550 .. and what this means is:
p (i.e. price per item) = 550/100 = 5.5
q (i.e. quantity in demand) = 100
Now substitute these values of p and q in equation (iv), :
100 = -2 x 5.5/5 + c ===> c = 102.2
Use this value in eqn (iv),
q = -2p/5 + 102.2 ..... this is the answer one... q as a liner function of p.
from which,
p = -5q/2 + 102.2x5/2 (simplify it) .... this is answer to second question.. i.e. p as a liner function of q.
NOTE: you should put complete question..
...
Disclaimer - it might be wrong... :)
Last edited: 05-Jan-11 04:47 PM
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