Question

4. Suppose a short-run total cost function is given by C= 600 + 40Q^0.3 + 5 Q^2:

(a) Find out the fixxed cost, variable cost, marginal cost, average variable cost and average total cost.

(b) Plot them in a diagram and interpret the relationship between average and marginal cost.

Answer 1

C = 600 + 40Q^0.3 + 5Q²

(a)

Fixed cost = 600

Variable cost (VC) = 40Q^0.3 + 5Q²

Marginal cost (MC) = dC/dQ = [(40 x 0.3) / Q^0.7] + 10Q = (12 / Q^0.7) + 10Q

Average variable cost (AVC) = VC / Q = (40 / Q^0.7) + 5Q

Average total cost (ATC) = C / Q = (600 / Q) + (40 / Q^0.7) + 5Q

(b)

Data table used:

Q	C	FC	VC		ATC	AVC	MC
0	600	600	0
1	645	600	45		645	45	22
2	669	600	69		335	35	27
3	701	600	101		234	34	36
4	741	600	141		185	35	45
5	790	600	190		158	38	54
6	848	600	248		141	41	63
7	917	600	317		131	45	73
8	995	600	395		124	49	83
9	1082	600	482		120	54	93
10	1180	600	580		118	58	102

Graph:

From the graph it is seen that when ATC is falling, MC is rising.