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BRUINS AT WORK

By using regression analysis on given data, we estimate total cost, revenue functions and establish profit function. Find optimal price and quantity. Graphs included.

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BRUINS AT WORK

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  1. Econ 106P Spring 2012 BRUINS AT WORK Iris Yu Ting HsuehPeter Sung PaeWen Shen LiJong Won Baek

  2. 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

  3. Total Cost Estimate

  4. 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

  5. Total Revenue Estimate

  6. 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 ( = PQ – TC). • Find optimum quantity and price by maximizing the profit.

  7. Profit Function Graphs

  8. 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

  9. 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

  10. 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.

  11. Profit Function Graphs

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