Question

A firm estimated its short-run costs using an average variable cost function of the form

AVC = a + bQ + cQ²

And obtained the following results. Total fixed cost is $1,500.        

DEPENDENT VARIABLE:	AVC	R-SQUARE	F-RATIO	P-VALUE ON F
OBSERVATIONS:	40	0.8273	88.65	0.0001
VARIABLE		PARAMETER ESTIMATE	STANDARD ERROR	T-RATIO	P-VALUE
INTERCEPT		38.05	11.87	3.21	0.0028
Q		-4.20	1.56	-2.69	0.106
Q2		0.30	0.09	3.33	0.0020

16. The estimated marginal cost function is:
    1. MC = 38.05 – 8.4Q + 0.9Q²
    2. MC = 38.05 – 2.1Q + 0.6Q²
    3.   MC = 38.05Q – 8.4Q² + 0.9Q³
    4. MC = 38.05Q – 2.1Q² + 0.1Q³

17. If the firm produces 20 units of output, what is estimated AVC?

1. $48.05
2. $74.05
3. $230.05
4. $242.05

18. If the firm produces 20 units of output, what is estimated total cost?
    1. $1,500
    2. $6,101
    3. $6,341
    4. $2,981

19. If the firm produces 10 units of output, what is estimated MC?
    1. $44.05
    2. $26.05
    3. $77.05
    4. $270.05

20. At what level of output is AVC minimum?
    1. 0.14
    2. 4.7
    3.     7
    4. 28

Answer 1

Estimated AVC = 38.05 - 4.2Q + 0.3Q²

TVC = AVC x Q = 38.05Q - 4.2Q² + 0.3Q³

TC = TVC + FC = 38.05Q - 4.2Q² + 0.3Q³ + 1,500

(1) (a)

Estimated MC = dTC/dQ = 38.05 - 8.4Q + 0.9Q²

(2) (b)

When Q = 20,

AVC = 38.05 - (4.2 x 20) + (0.3 x 20 x 20) = 38.05 - 84 + 120 = 74.05

(3) (d)

When Q = 20,

TVC = AVC x Q = 74.05 x 20 = 1,481

TC = 1,481 + 1,500 = 2,981

(4) (a)

When Q = 10,

MC = 38.05 - (8.4 x 10) + (0.9 x 10 x 10) = 38.05 - 84 + 90 = 44.05

(5) (c)

AVC is minimum when dAVC/dQ = 0

dAVC/dQ = - 4.2 + 0.6Q = 0

0.6Q = 4.2

Q = 7