Problem 7: Use A Cell Reference Or A Single Formula

Problemproblem 7 1use A Cell Reference Or A Single Formula Where Appro

The marketing department of Acme Inc. has estimated the following demand function for its popular carpet deodorizer, Freshbreeze: Q = 100 – 5p, where Q is the quantity of an 8 oz. box sold (in thousand units) and p the price of an 8 oz. box. The task involves calculating the point price elasticity of demand at various prices and identifying the elastic, inelastic, and unitary elasticity ranges along the demand curve using Excel.

Specifically, the assignment requires constructing a spreadsheet that employs cell references or single formulas to compute the price elasticity of demand at prices from $1 to $19. Additionally, the task involves pinpointing the price ranges where demand is elastic, inelastic, or has unitary elasticity by referencing the calculated elasticities directly in the worksheet. The instructions emphasize avoiding copying and pasting values or manually typing in results, instead focusing on cell references and formulas for dynamic calculation.

Paper For Above instruction

Understanding the concept of price elasticity of demand is fundamental in microeconomics, especially when analyzing how consumers respond to price changes. The demand function provided, Q = 100 – 5p, illustrates a linear relationship between price and quantity demanded, where an increase in price results in a decrease in quantity sold. To accurately analyze this relationship, calculating the point elasticity at various price points reveals how responsive demand is at different sections of the curve.

The point elasticity of demand at a particular price and quantity is defined as:

ε = (dQ/dp) × (p/Q)

where dQ/dp is the derivative of the demand function with respect to price. Given the linear demand function, dQ/dp = -5, which simplifies the calculation of elasticity at any point on the curve.

Using Excel, the first step involves setting up the demand function parameters and calculating the quantity demanded for each price point from $1 to $19. For each price p, quantity Q can be computed using a cell formula like = 100 - 5 * p, where p is referenced from a specific cell.

Next, the point elasticity is calculated in a dedicated column using the formula:

= (dQ/dp) * (p / Q)

Since dQ/dp is a constant (-5), the formula becomes:

= -5 * (p / Q)

To implement this dynamically in Excel, suppose the price p is in cell C10 and quantity Q in cell D10, then in cell E10, the elasticity is calculated as:

= -5 * (C10 / D10)

This formula is then copied down the column corresponding to prices from $1 to $19. The calculated elasticities allow identifying the ranges of elastic, inelastic, and unitary demand.

Demand is elastic where ε > 1, inelastic where ε < 1, and unitary when ε = 1. Based on the calculations, the elastic demand occurs at higher prices, and inelastic at lower prices. The specific ranges can be obtained by referencing the elasticity column and comparing values to 1.

In the context of this specific demand curve, the demand remains inelastic at low prices, becomes unitary at a midpoint, and turns elastic at higher prices. For the given demand function, the demand is inelastic for prices from $1 up to approximately $10, has unitary elasticity near $10, and becomes elastic beyond this point, up to $19.

Accurate identification of these ranges assists managers and policymakers in making informed decisions about pricing strategies to maximize revenue or control demand elasticity.

Conclusion

Through the use of cell references and formulas in Excel, this exercise demonstrates the practical application of elasticity calculations along a linear demand curve. It encapsulates the importance of dynamic and formula-driven analysis, eliminating manual calculations, and ensuring accuracy in identifying critical points along the demand spectrum. Such analyses form the backbone of effective pricing strategies rooted in economic theory.

References

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