Temple University

Department of Economics

Economics 615

Econometrics I

The following data is the basis for an essay on average total cost curves by F.M. Scherer (2001). The original data can be found in Hase (1917). The table provides data on two processes for printing sheet music at the end of the 18^th century: engraving or using movable type. In the engraving process a skilled craftsman carved the music (staff lines, notes, etc.) into a metal plate. A single plate was large enough to print two sheets of music and took 6 – 8 hours to carve. When the plate was finished it was inked, the plate was wiped to leave ink in the engraved recesses, and then paper was pressed against it. The process was repeated for each sheet of paper.

In the movable type process a compositor assembled the line of music from a specialized font. The notes, staff lines, etc. were raised from the slug on which they had been cast. The assembled lines of music were then locked in a metal frame. The type face was then inked and paper pressed onto it. The intermediate step of wiping the inked surface before printing is unnecessary in the movable type process. Hence, the marginal cost of producing typeset music should be lower than that for engraved music. However, engraved music produced a higher quality product.

1.a. Fit a simple linear regression to the data for each of the two printing processes. That is, estimate the parameters of

where Cost is total cost (= cost per sheet times quantity).

b. Evaluate your results on the basis of t-statistics and goodness of fit.

2.a. Estimate the parameters of the following model for each of the processes.

b. Evaluate your results on the basis of t-statistics and goodness of fit.

3.a. Estimate the parameters of the following model for each of the printing processes.

b. Evaluate your results on the basis of t-statistics and goodness of fit.

4.a. Estimate the parameters of the following model for each of the printing processes.

b. Evaluate your results on the basis of t-statistics and goodness of fit.

5.a.  For each of the four models, derive marginal cost for each process.

6.a. Of the four models you have fit to the data, which do you prefer? Why? Consider both the economics and the statistics.
b. In a table report the fixed costs for both processes for each of the four models to which the data was fitted. (Your table will have four rows and two columns, plus labels.)
c. For a given model are the set-up costs different for the two printing processes? Be sure to state your null and alternate hypothesis, clearly state your test statistic, state your chosen level of test, and state your conclusion.
d. Scherer suggests that the set-up cost for engraved music is 900 pfennig with a marginal cost of 5 pfennig.  Test these hypotheses for the linear and quadratic models.
e. Scherer also suggests that set-up costs for the linear and quadratic typeset model are 750 pfennig.  Test this hypothesis.
f. For the quadratic movable type model Scherer believes marginal cost to be 4.25 pfennig over the output range 100-200 sheets and to be 2.5 pfennig over the output range 800-1000 sheets.  Test this joint hypothesis.