Question

Refer to the cubic total cost (TC) function given in equation below Y_i=β_1+β_2 X_i+β_3 X_i^2+β_4 X_i^3 ……….

(1) (Y_i ) ̂=141.7667+63.4776X_i-12.9615X_i^2+0.9396X_i^3………..(2) se= (6.3753) (4.7786) (0.9857) (0.0591) R^2=0.9983 Y X 193 1 226 2 240 3 244 4 257 5 260 6 274 7 297 8 350 9 420 10 The marginal cost (MC) is the change in the TC for a unit change in output; that is, it is the rate of change of the TC with respect to output. (Technically, it is the derivative of the TC with respect to X, the output). Derive this function from regression (1) and (2) The average variable cost (AVC) is the total (TVC) divided by total output. Derive the AVC function from regression in (1) and (2) The average cost (AC) of production is the TC of production divided by total output. For the function given in regression (1) and (2), derive the AC function. Plot the various cost curves previously derived and confirm that they resemble the stylized textbook cost curves.

Answer 1

The regression model is , and the estimated model is .

The MC would be as or or .

The total variable cost would be as (since the constant is the fixed cost, which doesn't change with output) and the AVC would be as or or .

The average total cost would be as or or .

The graph is as below.

As can be seen, all the curves confirms with the usual textbook curves.The ATC is U-shaped, AVC is below the ATC with the same shape, and MC U-shaped and cuts AVC and ATC at their minimum.