Managerial Economics?

Question

Given the demand equation P=120-5Q derive equations for total revenue and marginal revenue.

Does anyone have any idea on these?

Answer 1

This is an easy one.

Just start pluggin in P which is price and Q which is quantity.

say P=100
Q=50

100=5(50)

they will give you one or both variables, then you can graph them

Answer 2

Revenue is defined as Price times Quantity:

R = P*Q = (120-5Q)*Q = 120Q-5Q^2

Marginal Revenue is defined as the change in Revenue per change in Quantity demanded:

MR = change in R/change in Q

If you know differential calculus, you can take the (partial) derivative of the Revenue with respect to Q and get the answer. If not, then you can follow these steps:

MR = [(R at Q+delta-Q)-(R at Q)]/delta-Q

where delta-Q is the change in Q or in other words, if the Q moves from Q1 to Q2, then delta-Q = Q2-Q1

MR = [(120*(Q+delta-Q)-5*(Q+delta-Q)^2) - (120Q-5Q^2)]/delta-Q

If you expand this, you will find the following:

MR = [120Q + 120*delta-Q - 5Q^2 - 10*Q*delta-Q - 5*delta-Q^2 - 120Q + 5Q^2]/delta-Q

MR = [120*delta-Q - 10*Q*delta-Q]/delta-Q

The stuff in the []s in the above equation is all that's left. All other terms cancel.

Now, dividing all this by delta-Q, we get:

MR = 120-10*Q

So, the Revenue curve is given by:

R = 120Q - 5Q^2

and Marginal Revenue is given by:

MR = 120 - 10Q

In general, if Price is given as follows:

P = a - bQ

Then Revenue is:

R = aQ - bQ^2

and Marginal Revenue is:

MR = a - 2bQ

Good luck!