Homework 4

Managerial Economics

Mana Komai Molle

1. The market demand curve for mineral water is P=15-Q. Suppose that there are two firms that produce mineral water, each with a constant marginal cost of 3 dollars per unit. Fill in the entries for each of the following duopoly models.
2. Cournot model (quantity competition).
3. Stackelberg model (quantity leadership).

Model                   Q₁           Q₂           Q             P             (Profit margin)₁                 (Profit margin)₂

Cournot

Stackelberg

Write up your analysis, and compare your answers.

The quantity produced by firm 1 is denoted by Q₁

The quantity produced by firm 2 is denoted by Q_2.

The total quantity produced in the market is denoted by Q.

The market price is denoted by P.

Profit margin is P-MC.

Determining Individual Calorie Needs

The Harris Benedict Equation is a formula that uses your BMR and then applies an activity factor to determine your total daily energy expenditure (calories).

The BMR formula uses the variables of height, weight, age and gender to calculate the Basal Metabolic Rate (BMR). This is more accurate than calculating calorie needs based on body weight alone. The only factor it omits is lean body mass and thus the ratio of muscle-to-fat a body has. Remember, leaner bodies need more calories than less leaner ones. Therefore, this equation will be very accurate in all but the very muscular (will underestimate calorie needs) and the very fat (will over-estimate calorie needs).

Harris Benedict Equation

For men,
BMR = 66.5 + (13.75 x kg) + (5.003 x cm) – (6.775 x age)

For women,
BMR = 655.1 + (9.563 x kg) + (1.850 x cm) – (4.676 x age)

1 inch = 2.54 cm.
1 kilogram = 2.2 lbs.

As recent as 2005, the ADA (American Dietetic Association) published a comparison of various equations. The Mifflin-St Jeor was found to be the most accurate, especially with young adults with more muscle mass and other obese:

 Mifflin-St Jeor equation

Men: RMR= (9.99 x weight in kg) + (6.25 x height in cm) – (4.92 x age) + 5.

Women: RMR= (9.99 x weight in kg) + (6.25 x height in cm) – (4.92 x age) – 161

Katch-McCardle Formula

This formula is a variation on the basic Mifflin-St Jeor equation that will base the equation on Fat Free Mass (FFM) or Lean Mass. This is more accurate for those who are leaner (and who know their body fat percentage!).

Men & Women:
BMR = 370 + (21.6 X lean mass in kg)

Where Fat Free Mass = Weight in kg – (Body Fat Percentage * Weight in kg).

After calculating the BMR, exercise is factored in. Depending on the exercise level chosen, the BMR will be multiplied by anything from 1.2 to 1.9.

1. If you are sedentary (little or no exercise) : Calorie-Calculation = BMR x 1.2
2. If you are lightly active (light exercise/sports 1-3 days/week) : Calorie-Calculation = BMR x 1.375
3. If you are moderately active (moderate exercise/sports 3-5 days/week) : Calorie-Calculation = BMR x 1.55
4. If you are very active (hard exercise/sports 6-7 days a week) : Calorie-Calculation = BMR x 1.725
5. If you are extra active (very hard exercise/sports & physical job or 2x training) : Calorie-Calculation = BMR x 1.9

This provides us with maintenance calories. To get the fat loss figure – 20% is subtracted. The extreme fat loss figure has 40% subtracted BUT – there is a “rock bottom” figure that equates to 8 calories per pound of body weight – the extreme fat loss will never be less than this amount.   To gain weight, you need to add calories/day based on the desired amount of weight to be gained.

1.  What equation did you use and why?

(Harris Benedict equation, no activity)

2. What was your calculated BMR? 

1630

3.  What activity level number did you use to multiply by your BMR to get your caloric needs?  How did you arrive at using this activity level?

(sedentary)

4.  What was your calculated caloric needs for a typical day? 

1630 x 1.2 = 1956

5.  How could you use the number you got to lose, gain, or maintain your weight?

(To get the fat loss -20%)