Question

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form and obtained the following resultsDEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON FOBSERVATIONS: 35 0.8713 108.3 0.0001VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 43.40 13.80 3.14 0.0036Q -2.80 0.90 -3.11 0.0039Q2 0.20 0.05 4.00 0.0004What is the estimated equation for average variable cost (AVC)?What is the estimated equation for short-run marginal cost (SMC)?What is the estimated equation for total variable cost (TVC)?At what level of output is AVC at its minimum point for Straker Industries?If Straker Industries produces 20 units of output, what is its estimated TVC, AVC and SMC?

Answer 1

Note: The organized table is attached as picture below

i. What is the estimated equation for average variable cost (AVC)?

Intercept value = 43.40, Parameter estimates of Q and Q2 = -2.80 & 0.20 respectively.

Hence, the estimated equation for AVC is:

AVC = 43.40 - 2.80Q + 0.20Q2

ii. What is the estimated equation for total variable cost (TVC)?

Similarly, the estimated equation for TVC is

= AVC * Q

= 43.40Q - 2.80Q2 + 0.20Q3

iii. At what level of output is AVC at its minimum point for Straker Industries?

AVC will attain its minimum value when its derivative is set = 0. This occurs when:

-2.80 = -0.40Q

Q = 7.

iv. What is the estimated equation for short-run marginal cost (SMC)?

SMC is the derivative of TVC, its estimated equation is given by:

= 43.40 - 5.60Q + 0.60Q2

iv. If Straker Industries produces 20 units of output, what is its estimated TVC, AVC and SMC?

TVC = 43.40Q - 2.80Q^2 + 0.20Q^3

TVC = 43.40(20) - 2.80(20)^2 + 0.20(20)^3

TVC = 868 - 1120 + 1600

TVC = 1348

At 20 unit of output, its estimated TVC is 1348

AVC = 43.40 - 2.80Q + 0.20Q^2

AVC = 43.40 - 2.80(20) + 0.20(20)^2

AVC = 43.40 - 56 + 80

AVC = 67.4

At 20 unit of output, its estimated AVC is 67.4

SMC = 43.40 - 5.60Q + 0.60Q^2

SMC = 43.40 - 5.60(20) + 0.60(20)^2

SMC = 43.40 - 112 + 240

SMC = 171.4

At 20 unit of output, its estimated SMC is 171.4.