Heritage Corporation

Suppose Heritage Corporation believes that its total variable costs follow a cubic
specification and so it estimates its average variable costs using the following
specification:
AVC = a + bQ + cQ2
The regression analysis produces the following computer output:
DEPENDENT VARIABLE: AVC R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 45 0.6145 33.47 0.0001
VARIABLE-PARAMETER ESTIMATE-STANDARD Error-T−RATIO-P−VALUE
Intercept-175.0-25.00-7.00-0.0001
Q–3.20-0.80–4.00-0.0003
Q²-0.08-0.01-8.00-0.0001

a) Do the estimated coefficients have the required signs to yield a U-shaped AVC curve? Discuss the significance using the p-values.

b) Heritage Corporation’s marginal cost function is

c) At what level of output does AVC reach a minimum? What is the value of AVC at its minimum?

d) Compute AVC and SMC when Heritage produces 8 units