Posted: April 27th, 2024

Perform a statistical analysis of its short-run production costs

CASE
#1
(BE CAREFUL!!!DATA SET
IS DIFFERENT THAN CLASS EXAMPLES!!!)

ABC Enterprises, Inc. produces less than 1% of the
world’s supply of 32 MB random access memory (RAM) chips for electronic
devices. ABC’s RAM chips perform according to globally accepted performance
standards for this type of silicon chip (i.e., its chips are just like every
other producers’ chips). ABC has hired
you to do undertake three tasks:
1.
Perform a statistical analysis
of its short-run production costs to estimate its total variable cost function,
average variable cost function, and marginal cost function. ABC believes its total
fixed costs will be $9,338 per month, so you do not need to estimateTFC.
2.
Recommend production levels and
forecast profits for two chip pricescenarios:
a.
The price of 32 MB RAM chips
reaches $62 per chip,and
b.
The price of 32 MB RAM chips
falls to $35 perchip.
3.
Determine the price below which
ABC should shut down operations in the short
run.

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ABC provides you with the following cost and output data
for the past 19 months. Over this time period, inflation has been so low that
you do not need to adjust the cost data for the effects of inflation (the CPI
rose only 0.4% over the 19 month time period). Monthly output of chips is given
in the second column, which is titled “Monthly production of finished product.”
Costs are reported in seven categories (some
are fixed costs and some are variable costs). HINT: Remember, cost items
are part of fixed costs if the costs do not vary with output, even though fixed
cost items may vary overtime.

Cost Items for
ABC Enterprises, Inc.

Month

Monthly production of finished product

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1.
a. Compute total variable cost
(TVC) by adding the appropriate columns of
cost items. Compute average
variable cost (AVC). [Remember that you
are given an estimate of ABC’s futuretotal
fixed costs ($9,338 per month).] Print out the 19 months of data on output (Q) and total variable cost (TVC) and average variable cost(AVC).
b.
Plot a scatter diagram of TVCon the vertical axis and Qon the horizontal axis. Does the
scatter diagram suggest a functional form for TVC? (try to fit a trend line)
Explainbriefly.
c.
Plot a scatter diagram of AVCon the vertical axis and Qon the horizontal axis. Does the
scatter diagram suggest a functional form for AVC? (Try to fit a trend line)
Explainbriefly.
d.
Estimate a quadratic AVCfunction. Present the estimated
equation and evaluate the regression results (i.e., discuss the algebraic signs
of the parameter estimates, the significance levels, and theR2).
e.
Evaluate the results of your
regression equation in part a.
Specifically discuss algebraic signs of parameters, statistical significance,
and goodness offit.

2.
a. How many chips should be produced (monthly) if world chip
prices are $62perchip? Forecast the ABC’s profit at this
outputlevel.
b.
How many chips should be
produced (monthly) if world chip prices are $35 per chip? Forecast the profit
at this outputlevel.

3.
At what price should ABC shut
down and produce no chips in the shortrun?

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