How do I figure out the total revenue and marginal revenue. Do I just multiply 20+q/200 by q getting 20q+q^2/200? If so, the partial derivative is 20+q/100? Equating that to 20+q/200 gets q=0. What's going on?

First of all, you got the marginal revenue (MR) right.

Then, you let MR = demand. That’s wrong that that is why your results don’t make any sense.

 

A monopoly will produce a quantity so that the marginal revenue = marginal cost. Use that quantity and demand curve (again) to get price .

We use the demand curve to determine the marginal revenue (MR) as follows (note that the demand curve has NOT changed): 

TR = P*Q = (122 - 0.25 * Q) * Q = 122*Q - 0.25*Q². 

Derivative with respect to Q = MR = TR' = 122 - 0.5*Q

Equate with the NEW marginal cost (MC): MR = MC -->

              122 - 0.5*Q = 20 + Q/200 --> Q ~ 202

Can someone help with parts E & F?  I got 100 for part C and 22 for part D?  Am I on target?

Regards,

Greg

Greg,

I have the same answers as you for parts C and D of the Module 13 Homework.

For Part E, use the price P=22 that you calculated in part D. Plug that value of P=22 into the market demand curve P=122-Q/4 and then solve for Q. That will tell you the total industry demand quantity Q.

For Part F, divide the industry quantity (which is your answer to part E) by each firm's quantity (which is your answer to part C) to find the total number of firms competing in this industry. I got an answer of 4 firms competing in the industry for Part F.

Can someone confirm the answers to Parts A & B, as my following answers for C and D don't match.

A:20q + q^2/100 + 100

B:20 + q/100 + 100/q

What am I doing wrong?  If these are right can someone go through C?

I came up with the same total cost and average cost curves as Rock.  I am also having a problem that when I solve for the quantity that minimizes average cost, that quantity does not produce equal prices using the Total and Marginal cost curves.  I'm getting Q=141.42, P=22.12 under total cost, and P=22.83 under marginal cost.  Where did we go wrong?

CornyLou,

1.  I believe you and Rock are correct in parts A and B. To get part C, you partially differentiate the answer to B, and set it equal to 0.  You should get 0 = 1/100 - 100/Q^2; therefore Q = 100.

2. Regarding getting different prices under the Total and Marginal cost curves.   I think the Marginal Cost Curve would more accurately be described as "short term marginal cost curve," and the Average Total Cost Curve could be called the "long term marginal cost curve."  Since we've taken into accout the 100 in Fixed Costs, and in the long run all costs are variable.  For part D we want to use the Average Total Cost Curve, as we want to take these fixed costs into account.