Need answers for questions 2c and down

1. You are the manager of a firm that sells 24 packs of coffee pods for coffee makers. You typically sell the 24-packs for $14 and sell an average of 3,912 per month. You decide to raise the price to $18 per 24-pack. When you do this your monthly sales fall to 1,956.
   1. (6 points) Assuming that your firms demand function is linear (i.e., takes the form QP=a-bP), calculate the linear demand function

Note: 3 points for each parameter (i.e., a and b)

Q= a-bP 3912= a-b(14) 1956= a-b(18)

1956-3912= a-a-18b+14b

-1956= -4b

B= 489

3912= a-489*14 3912= a-6846 a = 10758

2. (Markups and elasticities). The marginal cost (MC) of producing your product is $10
   1. (3 points) Calculate the markups at the two prices from question 1 above

Note: Use the formula for Lerners Index (Markup on Price) to calculate the markup

For P=14 For P=18

14-10/14 = 0.286 18-10/18 = 0.444

b.(3 points) Using the estimated demand curve from the previous question, calculate the point price elasticities of demand at the two price from question 1

-489 * 14/3912= -1.75

P= 14 Q=3912 then price elasticity is -1.75

-489 * 18/1956 = -4.5

When P= 18 and Q = 1956 then price elasticity is -4.5 -

c. (3 points) Use the markups and elasticities to work out whether the two prices are higher or lower than the profit maximizing price.

NOTE: YOU DO NOT NEED TO CALCULATE THE PROFIT MAXIMIZING PRICE YET. SEE THE MINI-LECTURE ON MARKUPS AND ELASTICITIES.

3. (Profit Maximization) Use the estimated demand function that you calculated in question 1 and the cost function below to work out the profit maximizing price.

TCQ=$9,604+$10Q

a.(3 points) Calculate the profit maximizing quantity

b.(3 points) Calculate the profit maximizing price