Microecon help monopoly?

Question

Consider the market for strawberry jam. Suppose there is only one producer and the market demand and supply are given by these eqns: D(p) = 100-2Pd, S(p) = 20 +6Ps, C(q) =q^2/12 -20/6q

Output is given by "y".

(i)What is the revenue function R(y)? is this PxQ where Q is y. so Py? but then P = (y-100)/2 from D(p)? or does it matter which expression I use D(p) or S(p)?

Answer 1

(i)

TR=P*Y

D(p)=Y

P(d)=P

Y=100-2P

P=50-Y/2

TR=50Y-(Y^2) /2

MR=(TR)' = 50-Y

TC=(Y^2)/12-20/(6Y)

MC=(TC)'=Y/6 -10/(3(Y^2))

To calculate total revenue you should take demand equation for monopolist (if monopolist modifies supply to fit required demand) - and in case if you are researching how revenue will be affected as effects of shifts in demand with fixed supply - then for revenue could be taken supply equation.

So all depends on what you are trying to figure out.