Requirement , please draw the graph to support answer B and C

Assignment # 6

Assignment for Unit 8 (Production & Cost Analysis)

Microsoft wants to estimate the average variable cost function of producing computer diskettes.The firm believes that AVC varies with the level of output and wages.Alan Anderson, the economist in the research department of the firm, collects monthly data on output (the number of diskettes produced), average variable costs, and wage rates paid by the firm over the past two years.He deflates costs and wages by their respective price indexes in order to eliminate inflationary influences.He then regresses total variable costs (TVC) on output (Q) and wages (W) and obtains the following result (where the numbers in parentheses are t values):

TVC = 0.14 + 0.80Q + 0.036W

(2.8)(3.8)(3.3)

= 0.92D - W = 1.9

(a) If W = $10, derive the AVC and MC functions of the firm.(25 points)

Plugging the given value of W:

TVC = 0.14 + 0.8*Q + 0.036*10,

TVC = 0.14 + 0.36 + 0.8*Q,

TVC = 0.5 + 0.8*Q-----(1)

AVC, average variable cost, is the variable cost spent on producing a typical unit. It is measured by the below formula:

AVC = TVC /Q, substituting values:

AVC = (0.5 + 0.8*Q)/Q,

AVC = 0.5/Q + 0.8 --(2)

The marginal cost function, which estimates extra costs spent on making another unit of output, is calculated as follows:

MC = d TVC / dQ, differentiate TVC with respect to Q:

MC = 0 + 0.8*1,

MC = 0.8.---(3)[J1]

The equation (3) is the function of MC.

(b) What are the shapes of the AVC and MC curves of the firm?(25 points)

We can state that marginal cost remains fixed and equal to 0.8 at all levels of output. In other words, it resembles a horizontal line. Whereas, the AVC function appears to be a decreasing function of output level that is more production benefits the firm in terms of lower variable cost per unit. [J2]

(c) Why did Anderson fit a linear rather than a quadratic or cubic TVC function? (25 points)

The decision of choosing linear function over other kinds of function is usually taken when we believe that there is a linear relationship between the variables. So, Anderson must have chosen a linear fit over cubic or quadratic curves thinking that that total variable cost (TVC) of the firm has a linear association with output and wages. Put it differently, cost structure of this firm might vary linearly with the level of output, which tempted him to choose the linear regression line.[J3]

(d) Was this the right choice?Why?(25 points)

We can verify whether the above regression model is the right option or not by examining the values of t-statistics and R^2.The t-values ( as given in the brackets) are greater than 2 , which implies that all of the independent variables are significant. In addition, the value of R^2is 0.92 (assumed what is given in second last equal sign is the value of R^2), which shows more than 90 % of the variation in the value of TVC is predicted by this linear model. Moreover, the value of D-W test is approximately equal to 2 indicating no auto correlation in the error term ( a must for linear regression model).[J4]