Econ 705 Module 2 Assignment

1. Your company utilizes both employees (L) and specialized robots (R) in its production process. The hourly wage of employees is $25, and the hourly cost of operating a robot is $175. The table below describes how the number of each type of input affects output or product (in a marginal way).

Number of employees (L)	Marginal product of labor (MPL)	Number of robots (R)	Marginal product of robots (MPR)
1	125	1	840
2	120	2	822.5
3	115	3	805
4	110	4	787.5
5	105	5	770
6	100	6	752.5
7	95	7	735

a. Given the much higher productivity of robots, why would the company ever consider using employees at all in its production?

b. When it started out, the company used three employees and five robots; is this an ideal combination of inputs? Why or why not?

c. During its busy season, the company increases its employees to five; provided it had a sufficient budget, what would be the optimal number of robots to use in this situation?

d. During the normal season when the company uses three robots, what would be the optimal number of employees to use?

2. Your company has estimated its total cost to be TC = 240,000 + 70Q + 0.01Q²; its marginal cost is thus MC = 70 + 0.02Q, where Q is the quantity of units produced and TC is in dollars. Since your market is relatively competitive, your company is able to sell its output for $220 each (which thus yields MR = 220 and TR = 220Q).

a. Produce a chart in Excel showing TC and TR with Q on the horizontal axis. Have Q go from 0 to 10,000 units (each row of your Q column can increase by a relatively large number so that your table isn't huge). Produce a second chart showing MC and MR with Q again on the horizontal axis.

b. What is the optimal level of output for your company to produce/sell? What is the marginal revenue from the last unit sold?

c. What are the total revenue, total cost, and profit (net benefit/net revenue/etc.) from selling the optimal number of units?

d. An eager intern at your company suggests that, since the company earns $220 revenue for each unit sold, then the company could make still more profit by selling more than the level chosen in part b; why would your company not want to produce and sell more output than the level you chose in part b?

3. Your company manufactures miniature agricultural structures with uplifting messages printed on them, for sale in bookstores ("Barns Ennoble"). You've collected data on annual sales (S, number of toy barns sold per year) the price of your toy barn (P, in dollars), and the population size in the different cities in which your company has retail locations (N, number of people; you currently only have one establishment in each city). You estimate the following regression model: S = a + bP + cN. In your regressions, you usually look for a 10%-or-better level of confidence.

a. What signs do you expect for a, b, and c?

b. Your regression yields the following results:

Adjusted R Square	0.831
Independent Variables	Coefficients	Standard Error	t Stat	P-value
Intercept	1882	258	7.298	0.00076
P	-47.09	7.95	-5.923	0.00196
N	0.0014	0.0011	1.347	0.23573

Interpret what these coefficients mean.

c. Does price have a statistically significant effect on sales?

d. Does population have a statistically significant effect on sales?

e. What portion of the total variation in sales remains unexplained?

f. Barns Ennoble is considering selling toy barns in a new city, where the population is 142,000, and setting its barn price at $32. What level of annual sales would you expect in this new city (rounded to the nearest unit)?

4. Download the "State Crime" Excel sheet; row 2 gives detailed descriptions of each variable, while row 4 gives short versions that should be used in your regressions. Estimate the following multiple regression models (remember that all of your independent variables will have to be in adjacent columns in Excel). Look at each set of results critically and consider how you would interpret the strengths and weaknesses of each model. Save your results from each model for use when completing the end-of-module assessment. Use "Robbery" as your dependent variable in each model. The notation f(X, Y, Z) means "a function of X, Y, Z; i.e., X, Y, and Z are your independent variables. Even though it isn't listed, each model will include an intercept. NOTE: when Excel reports a value like 2.4E-06, this is scientific notation for 2.4 * (10^-6), or 0.0000024.

Model A: Robbery = f(%Metro, %Poverty, Rain)

Model B: Robbery = f(PerCapIncome, %SameHouse, MedianAge)

Model C: Robbery = f(PerCapIncome, %SameHouse, MedAgeMale)

Model D: Robbery = f(PerCapIncome, %SameHouse, MedAgeFemale)

Model E: Robbery = f(PropCrime, %Bachelors+, %Unemploy, Temp)

Model F: Robbery = f(PropCrime, %Bachelors+, %Unemploy, Sun)

Model G: Robbery = f(PropCrime, %Bachelors+, %Unemploy, Rain)

The state of East Wyoming currently has a property crime rate of 2,250, a "%Bachelors+" rate of 35%, a "%Unemploy" rate of 3.2 (be sure to use 3.2 consistent with the underlying data, not 3.2% or 0.032; be careful of the units on all the variables), and an average temperature of 45 degrees. Recent changes in police activity have led to the property crime rate dropping to 2,000. This change will likely be associated with the Robbery rate changing from about 55.0 robberies (per 100,000 inhabitants) to about ___ robberies.