1. An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.35 in wasted wages. The agency decides to hire operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls).
Number of Operators
Total minutes of personal calls
a. What is the most the agency would be willing to pay the first operator?
b. If operators are paid $30 an hour, how many operators should the agency hire?
c. Assume that the cost of personal calls temporarily rises to $0.45 in wasted wages. If the operator wage is still $30/hour, how many operators should the agency hire now?
d. Assume a change in the operator labor market results in operator wages rising to $39 an hour; with the cost of personal calls back at the original $0.35 per minute, how would this affect the number of operators the agency should optimally hire?
2. Your company has estimated its total cost to be TC = 2000 + 7Q + 0.004Q2; its marginal cost is thus MC = 7 + 0.008Q, 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 $43 each (which thus yields MR = 43 and TR = 43Q).
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. 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 $43 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. You work at a company (Freeze Your Butt On®) that produces window air conditioning units. To gauge performance, you’ve utilized data on monthly sales (S) and the price of your most popular unit (P), both in dollars, as well as the daily average summer temperature in your most popular market (T) in degrees Fahrenheit. You estimate the following regression model: S = a + bP + cT. 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
Interpret what these coefficients mean.
c. Does our price have a statistically significant effect on our sales?
d. Does average temperature have a statistically significant effect on our sales?
e. What fraction of the total variation in our sales remains unexplained?
f. Our company is considering selling our most popular unit in a new city, where the average daily summer temperature is 72°, for a price of $325. What level of sales would you expect in this new city (rounded to the nearest dollar)?
4. Download the “Soft Drink Consumption” Excel sheet. 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. C, the dependent variable, will always be “Consumption of Soft Drinks per Capita;” for independent variables, use the following specifications. (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: C = f(food services, dentists, physicians)
Model B: C = f(% obese, % smokers total)
Model C: C = f(% obese, % male smokers, % female smokers)
Model D: C = f(% obese, % smokers total, % male smokers)
Model E: C = f(mean annual temp, per capita income)
Model F: C = f(mean annual temp, per capita income, physicians)
Model G: C = f(mean annual temp, per capita income, dentists)