Question

An office supply company manufactures and sells X permanent markers per year at a price of P €/unit. The Price/Demand equation
for the markers is:

Answer 1

$P=7-0.002x$

$$TC=1000+2x$$

$TR=PQ$ (Total revenue= Price $*$ Quantity

$(7-0.002x$ $)x$

$MR=$ $dTR\over dQ$ $=7x-0.002x{^2}$

$=7-0.004x$

$MC=$ $dTC\over dQ$ $=1000+2x$

$=2$

For profit maximization, marginal revenue = marginal cost.

$MC=MR$

$2=7-0.004x$

$x=1250$

$Price$

$P=7-0.002(1250)$

$=4.50$