### The Coconut Oil Demand FunctionThe coconut oil demand function (Bushena and Perloff, 1991) is given by:\[ Q = 1,200 - 9.5p + 16.2P_p + 0.2Y \]where - $ Q $ is the quantity of coconut oil demanded in thousands of metric tons per year,- $ p $ is the price of coconut oil in cents per pound,- $ P_p $ is the price of palm oil in cents per pound,- $ Y $ is the income of consumers.**Assumptions:**- The initial price of coconut oil ($ p $) is 65 cents per pound.- The price of palm oil ($ P_p $) is 31 cents per pound.- The demand ($ Q $) is 1,275 thousand metric tons per year.### Tasks:**1. Calculate the price elasticity of demand for coconut oil.** The formula for the price elasticity of demand (e) is:\[ e = \frac{dQ}{dP} \times \frac{P}{Q} \]**2. Calculate the cross-price elasticity of demand (with respect to the price of palm oil).** The formula for the cross-price elasticity of demand is:\[ e_{cross} = \frac{dQ}{dP_p} \times \frac{P_p}{Q} \]**Note:** Please round your responses to three decimal places and include a minus sign for the price elasticity of demand.### Example Calculation**Price Elasticity of Demand:**Applying the given function and assumptions, the necessary steps must be taken to derive the elasticity values appropriately. Follow the specific steps as per economic principles to reach to the desired answers. ### Detailed Diagram ExplanationWhile there is no graphical depiction in the excerpt, the verbalized steps ensure clarity on deriving the elasticities meticulously. It is recommended to visualize the elasticity on a graph where applicable, plotting price on the x-axis and quantity demanded on the y-axis for better understanding.### ConclusionFollowing these instructions and using the assumptions given, students can accurately determine the elasticity responses essential for understanding consumer behavior in relation to prices and alternative goods like palm oil.### Note- Ensure to show detailed steps in any calculations for accuracy.- Verify all responses are thoroughly rounded to three decimal places as instructed.

The coconut oil demand function is given below:Q = 1200 - 9.5p + 16.2pp + 0.2YWhere Q is the…

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The coconut oil demand function (Bushena and Perloff, 1991) is Q=1,200-9.5p+16.2pp +0.2Y,

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Question

### The Coconut Oil Demand Function

The coconut oil demand function (Bushena and Perloff, 1991) is given by:

\[
Q = 1,200 - 9.5p + 16.2P_p + 0.2Y
\]

where
- $ Q $ is the quantity of coconut oil demanded in thousands of metric tons per year,
- $ p $ is the price of coconut oil in cents per pound,
- $ P_p $ is the price of palm oil in cents per pound,
- $ Y $ is the income of consumers.

**Assumptions:**
- The initial price of coconut oil ($ p $) is 65 cents per pound.
- The price of palm oil ($ P_p $) is 31 cents per pound.
- The demand ($ Q $) is 1,275 thousand metric tons per year.

### Tasks:

**1. Calculate the price elasticity of demand for coconut oil.**

The formula for the price elasticity of demand (e) is:
\[ e = \frac{dQ}{dP} \times \frac{P}{Q} \]

**2. Calculate the cross-price elasticity of demand (with respect to the price of palm oil).**

The formula for the cross-price elasticity of demand is:
\[ e_{cross} = \frac{dQ}{dP_p} \times \frac{P_p}{Q} \]

**Note:** Please round your responses to three decimal places and include a minus sign for the price elasticity of demand.

### Example Calculation

**Price Elasticity of Demand:**

Applying the given function and assumptions, the necessary steps must be taken to derive the elasticity values appropriately. Follow the specific steps as per economic principles to reach to the desired answers.

### Detailed Diagram Explanation

While there is no graphical depiction in the excerpt, the verbalized steps ensure clarity on deriving the elasticities meticulously. It is recommended to visualize the elasticity on a graph where applicable, plotting price on the x-axis and quantity demanded on the y-axis for better understanding.

### Conclusion

Following these instructions and using the assumptions given, students can accurately determine the elasticity responses essential for understanding consumer behavior in relation to prices and alternative goods like palm oil.

### Note

- Ensure to show detailed steps in any calculations for accuracy.
- Verify all responses are thoroughly rounded to three decimal places as instructed.

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