The function Q = F(p,ps,y) describes how the monthly demand, Q (measured in 100s of Widgets), for Grinch Inc. Widgets depends on the variables: • p = the price/Widget that Grinch Inc. sets (measured in S). • Ps= average price of substitutes for Grinch Inc. Widgets (measured in $). • y = average disposable income in the market for Widgets (measured in $1000s). When average disposable income in the market is $4200 and Grinch Inc.s price is $12 and the average price of substitutes is $11... · Q = 66 Op=-0.28 2ps = 0.52 Qy = 0.31 If average monthly income increases to $4400 and the average price of substitutes increases to $11.35, by approximately how much can Grinch Inc. increase their price while keeping demand for their Widgets fixed at Q = 66 ? Ο Δρ = 0.87 O There is no way to estimate this from the given information.. O Ap = 0.53 O Ap = 0.72 .

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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**Understanding the Demand Function for Grinch Inc. Widgets**

The function \( Q = F(p, p_s, y) \) describes how the monthly demand, \( Q \) (measured in 100s of Widgets), for Grinch Inc. Widgets depends on the variables:
- \( p \) = the price/Widget that Grinch Inc. sets (measured in $).
- \( p_s \) = average price of substitutes for Grinch Inc. Widgets (measured in $).
- \( y \) = average disposable income in the market for Widgets (measured in $1000s).

When the average disposable income in the market is $4200 and Grinch Inc.'s price is $12, and the average price of substitutes is $11:
- \( Q = 66 \)
- \( Q_p = -0.28 \)
- \( Q_{ps} = 0.52 \)
- \( Q_y = 0.31 \)

### Problem Statement
If average monthly income increases to $4400, and the average price of substitutes increases to $11.35, by approximately how much can Grinch Inc. increase their price while keeping the demand for their Widgets fixed at \( Q = 66 \)?

### Potential Answers

- \( \Delta p \approx 0.87 \)
- There is no way to estimate this from the given information.
- \( \Delta p \approx 0.53 \)
- \( \Delta p \approx 0.72 \)

To solve this, one would typically need to use calculus and algebra to manipulate the demand function, considering how changes in each of the variables affect \( Q \). Calculating the specific impact of changes in \( y \) and \( p_s \) would provide insight into how much \( p \) can be adjusted.

This type of problem helps students understand the relationship between different economic variables and how changes in one can impact another.
Transcribed Image Text:**Understanding the Demand Function for Grinch Inc. Widgets** The function \( Q = F(p, p_s, y) \) describes how the monthly demand, \( Q \) (measured in 100s of Widgets), for Grinch Inc. Widgets depends on the variables: - \( p \) = the price/Widget that Grinch Inc. sets (measured in $). - \( p_s \) = average price of substitutes for Grinch Inc. Widgets (measured in $). - \( y \) = average disposable income in the market for Widgets (measured in $1000s). When the average disposable income in the market is $4200 and Grinch Inc.'s price is $12, and the average price of substitutes is $11: - \( Q = 66 \) - \( Q_p = -0.28 \) - \( Q_{ps} = 0.52 \) - \( Q_y = 0.31 \) ### Problem Statement If average monthly income increases to $4400, and the average price of substitutes increases to $11.35, by approximately how much can Grinch Inc. increase their price while keeping the demand for their Widgets fixed at \( Q = 66 \)? ### Potential Answers - \( \Delta p \approx 0.87 \) - There is no way to estimate this from the given information. - \( \Delta p \approx 0.53 \) - \( \Delta p \approx 0.72 \) To solve this, one would typically need to use calculus and algebra to manipulate the demand function, considering how changes in each of the variables affect \( Q \). Calculating the specific impact of changes in \( y \) and \( p_s \) would provide insight into how much \( p \) can be adjusted. This type of problem helps students understand the relationship between different economic variables and how changes in one can impact another.
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