Question

Smelling of Tulips, Inc., a perfume company, estimated its short-run costs using a U-shaped average variable cost function of the form and obtained the following results. Total fixed cost (TFC) at S.T. Inc. is $1290. Adjusted R Square 0.809 Coefficients Standard Error t Stat P-value Intercept 47.66 3.29 14.49 0.0001 Q -4.67 0.72 -6.48 0.0000 Q^2 0.26 0.03 7.79 0.0000 a. What level of output (Q) is associated with the minimum AVC

Answer 1

The level of output (Q) is associated with the minimum AVC is 8.98.

Step-by-step explanation:

The following sorted data are given in the question:

Adjusted R Square 0.809

Coefficients Standard Error t Stat P-value

Intercept 47.66 3.29 14.49 0.0001

Q -4.67 0.72 -6.48 0.0000

Q^2 0.26 0.03 7.79 0.0000

From the regression results above, the regression equation for AVC can be obtained as follows:

AVC = Coefficient of intercept + Coefficient of Q * Q + Coefficient of Q^2 * Q^2 …………. (1)

Substituting the relevant values into equation (1), we have:

AVC = 47.66 – 4.67Q + 0.26Q^2

Differentiate AVC with respect to Q, equating it to 0, and solve for Q, we have:

dAVC/dQ = -4.67 + (2 * 0.26)Q = 0

4.67 = 0.52Q

Q = 4.67 / 0.52

Q = 8.98

Therefore, the level of output (Q) is associated with the minimum AVC is 8.98.