Transcript bruins at work

Econ 106P Spring 2012
BRUINS AT WORK
Iris Yu Ting Hsueh
Peter Sung Pae
Wen Shen Li
Jong Won Baek
Using the Given Data
• By using regression analysis on the given data, we were
able to estimate the total cost and total revenue functions.
We then established the profit function by combining the
total cost and total revenue functions. With the profit
function, we can maximize it to find the optimal price and
the quantity.
• Steps are shown in the following slides
Total Cost Estimate
%change
in out put
-20
-10
0
10
20
output
q
2000
2250
2500
2750
3000
q^2
4000000
5062500
6250000
7562500
9000000
change in
TC
-5250
-2500
0
2450
4700
TC
34750
37500
40000
42450
44700
Total Cost: Linear vs Quadratic
• TC=15030+9.94*Q
• R-square: .9987
• TC= 7680+15.94*Q-.0012*Q^2
• R-square: .999968
• Quadratic regression turned out to be more accurate
Total Revenue Estimate
%chang
in price
-20
-10
0
10
20
p
16
18
20
22
24
change in
sales
1500
500
0
-400
-800
q
4000
3000
2500
2100
1700
TR
64000
54000
50000
46200
40800
Price and Quantity relationship
• The relationship between price and quantity is:
P=37.387-.00965Q+.00000107Q^2
(found by regression analysis)
• And since TC = 7680+15.94*Q-.0012*Q^2,
• We can substitute the above equations into the profit
function ( 𝜋 = PQ – TC).
• Find optimum quantity and price by maximizing the profit.
Profit Function Graphs
18000
16000
14000
12000
10000
profit1
profit2 substituting p
profit2
8000
profit1 substituting p
6000
4000
2000
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Recommended Price (Part A & B)
• Using the data given by the production and marketing
managers, the optimal price is $16, which will generate
the highest profit, as shown by the profit graph.
• A 10 % increase in the demand at all prices will also result
in an optimal price of $16 because it is a simple shift in
quantity demanded at every price level
Recommended Price (Part C)
• It is more difficult to accurately predict the price and
quantity if the change in price is further away from the
original price ($20).
• In addition, quadratic regression is only accurate within a
limited range
Recommended Price (Part C)
• If the estimates given by the sales manager were a bit too
optimistic, our price recommendation would be the
following:
By maximizing the profit function, the optimum price
is $21.66 and the quantity is 2134, which results in a
profit of $10,006
• note: optimistic as in the marketing manager is confident
in predicting consumer’s reactions to the changes in
price, even if the change is large.
Profit Function Graphs
18000
16000
14000
12000
10000
profit1
profit2 substituting p
profit2
8000
profit1 substituting p
6000
4000
2000
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000