Questions: The new business Venture, Best-in-World, has been manufacturing technology devices for over 20 years and is considering adding a new technology device to its music line. They have an established reputation for building quality devices, but they are rather novice in the music industry. The Chief Innovation and Design Officer, Julie Naugle-Hall, is tasked with hiring a marketing firm to conduct a survey to determine the feasibility and demand for their new music device. The decision table illustrates the potential profits for high demand, moderate demand, and low demand for the new music device. The decision will be whether to start production on this new device in small scale, large scale or not at all. Decision Table: Alternatives High Demand of Nature Moderate Demand Low Demand Small-scale production 950,000 250,000 -500,000 Large-scale production 1,700,000 600,000 -1,000,000 No production 0 0 0 Probabilities 0.20 0.30 0.50 How much should Julie be willing to pay a marketing firm to conduct the survey for probability information regarding the feasibility and demand for their new music device?

The new business Venture, Best-in-World, has been manufacturing technology devices for over 20 years and is considering adding a new technology device to its music line. They have an established reputation for building quality devices, but they are rather novice in the music industry. The Chief Innovation and Design Officer, Julie Naugle-Hall, is tasked with hiring a marketing firm to conduct a survey to determine the feasibility and demand for their new music device. The decision table illustrates the potential profits for high demand, moderate demand, and low demand for the new music device. The decision will be whether to start production on this new device in small scale, large scale or not at all. Decision Table: Alternatives High Demand of Nature Moderate Demand Low Demand Small-scale production 950,000 250,000 -500,000 Large-scale production 1,700,000 600,000 -1,000,000 No production 0 0 0 Probabilities 0.20 0.30 0.50 How much should Julie be willing to pay a marketing firm to conduct the survey for probability information regarding the feasibility and demand for their new music device?
Transcript text: The new business Venture, Best-in-World, has been manufacturing technology devices for over 20 years and is considering adding a new technology device to its music line. They have an established reputation for building quality devices, but they are rather novice in the music industry. The Chief Innovation and Design Officer, Julie Naugle-Hall, is tasked with hiring a marketing firm to conduct a survey to determine the feasibility and demand for their new music device. The decision table illustrates the potential profits for high demand, moderate demand, and low demand for the new music device. The decision will be whether to start production on this new device in small scale, large scale or not at all. \begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{4}{|c|}{ Decision Table } \\ \hline & \multicolumn{3}{|c|}{} \\ \hline Alternatives & High Demand of Nature & Moderate Demand & Low Demand \\ \hline Small-scale production & 950,000 & 250,000 & $-500,000$ \\ \hline Large-scale production & $1,700,000$ & 600,000 & $-1,000,000$ \\ \hline No production & 0 & 0 & 0 \\ \hline Probabilities & 0.20 & 0,30 & 0,50 \\ \hline \end{tabular} How much should Julie be willing to pay a marketing firm to conduct the survey for probability information regarding the feasibility and demand for their new music device?
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Solution

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Solution Steps

Step 1: Identify the Expected Monetary Value (EMV) for Each Alternative

Calculate the EMV for each production alternative by multiplying the payoff for each state of nature by its probability and summing the results.

  • Small-scale production: \[ EMV_{\text{small}} = (950,000 \times 0.20) + (250,000 \times 0.30) + (-500,000 \times 0.50) = 190,000 + 75,000 - 250,000 = 15,000 \]

  • Large-scale production: \[ EMV_{\text{large}} = (1,700,000 \times 0.20) + (600,000 \times 0.30) + (-1,000,000 \times 0.50) = 340,000 + 180,000 - 500,000 = 20,000 \]

  • No production: \[ EMV_{\text{none}} = (0 \times 0.20) + (0 \times 0.30) + (0 \times 0.50) = 0 \]

Step 2: Determine the Best Alternative Based on EMV

Compare the EMVs calculated in Step 1 to determine the best alternative.

  • Small-scale production: $15,000
  • Large-scale production: $20,000
  • No production: $0

The best alternative is large-scale production with an EMV of $20,000.

Step 3: Calculate the Expected Value of Perfect Information (EVPI)

EVPI is the difference between the expected value with perfect information and the best EMV without perfect information.

  • Expected value with perfect information: \[ EV_{\text{perfect}} = (1,700,000 \times 0.20) + (600,000 \times 0.30) + (0 \times 0.50) = 340,000 + 180,000 + 0 = 520,000 \]

  • EVPI: \[ EVPI = EV_{\text{perfect}} - \text{Best EMV} = 520,000 - 20,000 = 500,000 \]

Final Answer

Julie should be willing to pay up to $500,000 to the marketing firm for the survey.

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