Need to check my work for solving the problem Monopolistic p

Need to check my work for solving the problem: Monopolistic product: Qty: Price = 0, $120; 1, $105, 2, $90; 3, $75; 4, $60; 5, $45; 6, $30. The ATC = $45/unit, constant MC constant.

TR = P*Q and MR = Change TR/ Change Q.

1) Profit-maximizing level of output and the price = MR=MC, or qty 3 at $75.. is that correct?

2) Lerner Index = P - MC/ P = 75-45/75 = .4   is that correct?

Solution

(1) correct.

When Q = 2, P = $90, TR = 2 x $90 = $180

When Q = 3, P = $75, TR = 3 x $75 = $225

So, at Q = 3, MR = $(225 - 180) = $45

Here, ATC = MC = $45 (Since additional cost information is not given)

So, MR = MC at Q = 3 is the profit maximizing level.

(2) Correct.

LI = $(75 - 45) / $75 = $30 / $75 = 0.4

Congrats on getting both correct!