Question

A firm has a long-run total cost function: LT C(Q) = Q^ 3 − 20Q^2 + 220Q Derive expressions for long-run average cost and marginal cost, and sketch these curves. Plaese give the sketch

Answer 1

Long run Average Cost function is given by

Long run Marginal Cost can be obtained by differentiating LTC(Q) with respect tp Q, we get

We can develop the following schedule with the help of given equations

Q	LTC	LATC	LMC
0	0
1	201	201	183
2	368	184	152
3	507	169	127
4	624	156	108
5	725	145	95
6	816	136	88
7	903	129	87
8	992	124	92
9	1089	121	103
10	1200	120	120
12	1488	124	172
14	1904	136	248
16	2496	156	348