Econ question help (1 Viewer)

[Dimsimmer]

Hey guys, i have some trouble working out this question.

Suppose a firm is the only domestic producer of a commodity and that there are no imports of the good. The firm's total cost and demand curves are given be the following 2 equations:

TC: 6Q + .05Q^2 : Q = 360 - 20P

Where Q is the number of units produced each week and P is the price per unit

a) Calculate the price, quantity produced, and the firm's profit when profit is maximised.

Thanks for your help.

 

[jake2.0]

It's been a while since Micro, so this may not be right.

I remember that profit is max when marginal revenue (MR) = marginal cost (MC)

We know Total revenue = P.Q = Q.((360-Q)/20)

so MR = 18 - Q/10 (just derivative of TR)

and MC = 6 + Q (derivative of TC)

equating these two i got Q = 13 1/3

so P = 17 1/3 (from given eq Q = 360 - 20P)

and then use TP = TR - TC

 

[Dimsimmer]

Isn't MC equals to 6+.01Q because TC= 6Q+0.05Q^2, not 0.5Q^2. Dont worry about trying to work it out for me because i reckon i got the answer already. Thanks for your help.