Initial values are: PX = $9500 PY = $10000 I = $15000 A = $170000 W = 160 This function is: Qs = 89830 -40PS +20PX +15PY +2I +.001A +10W 1.(a). Use the above to calculate the arc price elasticity of demand between PS = $9000 decreasing to PS = $8000. The arc elasticity formula is: 1.(b). Judging from the computation in (a), do you expect the revenue resulting from the decrease in Ps to $8000 to increase, remain the same, or decrease relative to the revenue at Ps = $9000. (Hint: see the table on page 65 of Truett). Explain your choice. 1.(c). Calculate the point elasticity of demand for Smooth Sailing sailboats at PS = $9000 (which should make Qs = 101600). The formula is:
All questions utilize the multivariate
Initial values are: PX = $9500 PY = $10000 I = $15000 A = $170000 W = 160
This function is: Qs = 89830 -40PS +20PX +15PY +2I +.001A +10W
1.(a). Use the above to calculate the arc
1.(b). Judging from the computation in (a), do you expect the revenue resulting from the decrease in Ps to $8000 to increase, remain the same, or decrease relative to the revenue at Ps = $9000. (Hint: see the table on page 65 of Truett). Explain your choice.
1.(c). Calculate the point elasticity of demand for Smooth Sailing sailboats at PS = $9000 (which should make Qs = 101600). The formula is:
1.(d). Does this elasticity value indicate that Smooth Sailing demand is relatively responsive to changes in the price of these sailboats? Explain why or why not.
1.(e). Calculate the point “motorboat” price elasticity of demand when Py = $10000. Use Qs corresponding to PS = $9000 which should make Qs = 101600. Other variables and their values are given at the top, before question #1. The formula is:
1.(f). Does this elasticity indicate that the demand for Smooth Sailing’s boats is relatively responsive to changes in the price of Company Y’s motorboats? Explain why or why not.
1.(g). Calculate the point income elasticity of demand assuming I = $15000 and that Ps = $8500 (this should make QS = 431,600) and that the other variables are as given at the top before #1. The formula is:
1.(h). Does this elasticity coefficient indicate that the demand for Smooth Sailing boats is relatively responsive to changes in advertising expenditures? Explain why or why not.
1.(i). Weather
1.(j). Does this elasticity coefficient indicate that the demand for Smooth Sailing boats is relatively responsive to changes in income? Explain why or why not.
![**Elasticity Calculation for Demand Analysis**
The elasticity of demand, \( E_A \), is expressed by the formula:
\[
E_A = \frac{\partial Q_S}{\partial W} \cdot \frac{W}{Q_S}
\]
where:
- \( \frac{\partial Q_S}{\partial W} \) is the partial derivative of the quantity demanded with respect to income (W),
- \( W \) is the income,
- \( Q_S \) is the quantity demanded.
**Question 1(j):**
Does this elasticity coefficient indicate that the demand for Smooth Sailing boats is relatively responsive to changes in income? Explain why or why not.
*Elasticity7.docx 060272022*
**Explanation:**
In this context, elasticity measures how sensitive the quantity demanded of Smooth Sailing boats is to changes in consumer income. If the elasticity coefficient is greater than 1, the demand is considered elastic, meaning that demand is highly responsive to income changes. If it is less than 1, demand is inelastic, indicating less sensitivity to income changes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18689286-78bc-47d5-8a3d-145ab24af1f7%2F4d820db6-6b37-44e8-be8b-0fc1c2a9eed3%2F91xyh2b_processed.png&w=3840&q=75)
![# Price Elasticity and Demand Analysis for Smooth Sailing Sailboats
## Initial Values
- **\( P_X \):** $9500
- **\( P_Y \):** $10000
- **\( I \):** $15000
- **\( A \):** $170000
- **\( W \):** 160
**Function for Quantity Supplied:**
\[ Q_S = 89830 - 40P_S + 20P_X + 15P_Y + 2I + 0.001A + 10W \]
### 1(a). Arc Price Elasticity of Demand
Calculate the arc price elasticity of demand between a price drop from \( P_S = $9000 \) to \( P_S = $8000 \).
**Arc Elasticity Formula:**
\[ E_P = \frac{\Delta Q}{\Delta P} \cdot \frac{P_1 + P_2}{Q_1 + Q_2} \]
### 1(b). Revenue Expectations
Analyze whether the revenue at \( P_S = $8000 \) increases, remains constant, or decreases compared to the revenue at \( P_S = $9000 \). Refer to the table on page 65 of Truett for your explanation.
### 1(c). Point Elasticity of Demand
Calculate the point elasticity of demand at \( P_S = $9000 \) where \( Q_S = 101600 \).
**Point Elasticity Formula:**
\[ E_P = \frac{\partial Q_S}{\partial P_S} \cdot \frac{P_S}{Q_S} \]
### 1(d). Demand Sensitivity
Does the elasticity value suggest that demand is responsive to price changes of these sailboats? Provide a justification.
### 1(e). Motorboat Price Elasticity
Determine the point "motorboat" price elasticity of demand at \( P_X = $10000 \) using \( Q_S = 101600 \).
**Elasticity Formula for Motorboats:**
\[ E_{SY} = \frac{\partial Q_S}{\partial P_Y} \cdot \frac{P_Y}{Q_S} \]
### 1(f). Cross-Price Elasticity
Evaluate if demand for Smooth Sailing's boats is responsive to price changes in Company Y’s motorboats.
### 1(g). Income Elasticity of Demand
Calculate the point income elasticity of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18689286-78bc-47d5-8a3d-145ab24af1f7%2F4d820db6-6b37-44e8-be8b-0fc1c2a9eed3%2F3rt3fug_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
