Assume Caspian is a firm operating in a competitive market. The estimated its average variable cost function is shown below: AVC = A + BQ + CQ2
The total fixed cost (TFC) = $1,000.
Dependent VARIABLE AVC R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS 35 0.8713 108.3 0.0001
VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE
INTERCEPT 43.4 13.8 3.14 0.0036
Q -2.8 0.9 -3.11 0.0039
Q2 0.2 0.05 4 0.0004
a. Are the estimated coefficients statistically significant at the 5% level of significance?
b. Find the total cost function.
c. Find the equation for the ATC. Is it U-shaped? A simple yes/no is not enough. Use math.
d. Find the shut-down price.
e. How much will the firm produce at the market price of $53.4?
(a) p- values of the coefficients are < 0.05. Hence they are significant at 5% level of significance.
(b) AVC = 43.4 - 2.8Q + 0.2Q^2