ECON10005 QUANTITATIVE METHODS 1
Assignment 2
Semester 1, 2014
This assignment has three questions, and is due by 4.00pm on Thursday April 17.
It is to be submitted electronically as a .pdf file using the assignment tool on the subject’s LMS page. Marks depend on your tutor being able to understand your statements and arguments, so marks may be deducted for poor presentation or unclear language. Use nothing smaller than 12 point font. If you wish to write your assignment by hand and scan the file into a .pdf format, you may, though any illegible content will not be marked. Note that you can only submit one file, and cannot submit a file larger than around 4 megabytes.
You may work in groups of up to 4 students from the same allocated tutorial. Groups should nominate one student to submit the assignment for the whole group, with each student’s name and student number included in the document.
This assignment has a total of 40 marks available and may contribute up to 10% of your final mark in this subject.
1. A manufacturing company is reviewing the salaries of its full-time employees below the executive level at a large plant. The clerical staff is almost entirely female, while a majority of the production workers and technical staff is male. As a result the distributions of salaries for male and female emploees may be quite different. Table 1 gives the counts and percentages of women and men in each salary class. Using this data, calculate means and variances, together with the interquartile range, for each of the two groups of workers. (Indicate how you have obtained these values.) Using this information, what conclusions can you draw about the relative salary scales of the men and women working for this manufacturer. (10 marks)
2. Suppose that you are working with survey data where one of the questions asks the gender of the respondent. The answer is coded as a 1 if the respondent is male and a 0 if they are female. So, if there are n respondents to the survey, the data set will look something like

n data points
Show that, with such a data set, the least squares measure of location is the proportion of men in the data set. (A complete answer must begin with a statement of the criterion to be optimized, and then proceed from there.) (4 marks) Table 1: Salary Distributions of Female and Male Workers in a Large Factory
Salary Women Men


3. A production function is an equation specifying the relationship between the factor inputs to a production process and the output of that process. Marginal factor products are then the partial derivatives of output with respect to each of the factor inputs. Suppose that we wish to model the production function for a particular product and we have two competing specifications, one linear and the other log-log:
Qi = ß0 + ß1Ki + ß2Li + ei, i = 1,2,...,n. (1)
and
(2)
where Qi denotes the output from the ith firm, Ki denotes the quantity of capital used in the production process by the ith firm, and Li denotes the quantity of labour used in the production process. The ei and i denotes the error terms for each equation, respectively.
The file Prod.xlsx contains sets of observations on (Ki,Li,Qi) for each of 33 firms who each manufacture the same product. The units of Ki and Li are hundreds of dollars and the units of Qi are thousands of dollars.
(a) Fit the models specified in equations (1) and (2) using this data and report the results in the form of an equation.
Hint: In order to fit equation (2), you will need to create the data values for lnQi, lnKi, and lnLi using Excel’s commands. (4 marks)
(b) Interpret the least squares values of the coefficients in each equation. (6 marks)
(c) Calculate and interpret the coefficient of determination for each model.
(4 marks)
(d) On the basis of your fitted values from part 3(a), evaluate the marginal products of capital and labour in each of the two models. (6 marks)
(e) On the basis of your fitted values from part 3(a), evaluate the elasticities of output with respect to capital and labour — at K, L, and Q — in each of the two models. (6 marks)