Expert: Ahmed Salami - 11/4/2011

Question
A manufacturer determines that the supply function for x units of a particular commodity is S9x)=ln (x+2) and the corresponding demand function is D(x)= 10- ln(x+1).

Find the level of production and unit price that correspond to market equilibirum (where supply=demand).


The answer is:
xe=147
pe=$5

but I need help with the steps to get there thanks!

Answer
Hi Kristen,
S(x) = ln(x+2)
D(x) = 10 - ln(x+1)
There is market equilibrium when S(x) = D(x), i.e
ln(x+2) = 10 - ln(x+1)
ln(x+2) + ln(x+1) = 10
ln[(x+2)(x+1)] = 10
(x+2)(x+1) = e^10
x² + 3x + 2 = e^10
x² + 3x - (e^10 - 2) = 0

Solving the quadratic equation gives a positive value of x of about e^5, actually 146.92, and S(x) = D(x) = 5.
Note that we discard the negative solution of x because its not in the domain of our functions.

Regards