Weekly Sales Of Honolulu Red Oranges 425587

the Weekly Sales Of Honolulu Red Oranges Is Given Byq111618pcalcu

The weekly sales of Honolulu Red Oranges is given by the demand function q = 1116 − 18 p. The task involves calculating the price elasticity of demand at a specific price point, interpreting that elasticity, finding the price that maximizes weekly revenue, and computing the maximum revenue.

Paper For Above instruction

The demand function for Honolulu Red Oranges is expressed as q = 1116 − 18 p, where q represents weekly sales and p is the price per orange in dollars. To address the various components of this assignment, we begin by calculating the price elasticity of demand at a given price point, specifically when p = $31. Subsequently, we interpret what the calculated elasticity signifies regarding consumer responsiveness and analyze the price point that yields maximum revenue along with the corresponding revenue.

Calculating Price Elasticity of Demand at p = $31

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. It is calculated using the formula:

E = (dQ/dP) * (P/Q)

Given the demand function q = 1116 − 18 p, the derivative of q with respect to p is constant:

dQ/dP = -18

At p = $31, the quantity demanded (Q) is:

Q = 1116 − 18 * 31 = 1116 − 558 = 558

Therefore, the price elasticity of demand at p = $31 is:

E = (-18)  (31 / 558) ≈ -18  0.0554 ≈ -1.0

The negative sign indicates the inverse relationship between price and demand, consistent with typical demand behavior. The magnitude of approximately 1.0 suggests that demand is perfectly elastic at this point, meaning a 1% increase in price would lead to roughly a 1% decrease in quantity demanded.

Interpretation of the Elasticity

An elasticity of about -1.0 signifies unit elasticity, meaning that at this price level, consumers' demand responds proportionally to price changes. Specifically, a 1% increase in price results in a 1% decrease in quantity demanded, and vice versa. This level of elasticity indicates that the firm can influence total revenue by adjusting the price; raising the price would decrease total revenue, while lowering it would increase total revenue, assuming other factors remain constant.

Finding the Price That Maximizes Weekly Revenue

Total weekly revenue (TR) is given by:

TR = p * q

Plugging the demand function into the revenue formula:

TR(p) = p * (1116 − 18 p) = 1116 p − 18 p^2




To find the price that maximizes revenue, differentiate TR(p) with respect to p and set the derivative equal to zero:



d(TR)/dp = 1116 − 36 p = 0





Solving for p:



p = 1116 / 36 = 31





The revenue is maximized at a price of approximately $31 per orange.



Calculating the Maximum Revenue



Substituting p = $31 into the revenue function:



TR(31) = 1116  31 − 18  (31)^2


= 34,596 − 18 * 961


= 34,596 − 17,298


= 17,298





Thus, the maximum weekly revenue is $17,298 when the price of an orange is approximately $31.



Summary



In conclusion, at the price point of $31, the demand for Honolulu Red Oranges exhibits unit elasticity, implying that demand responds proportionally to price changes. The optimal price for maximum weekly revenue is $31, resulting in a maximum revenue of $17,298. This analysis helps the seller understand how pricing strategies influence both demand and revenue, enabling more informed decisions to optimize sales performance.



References
  • McConnell, C. R., Brue, S. L., & Flynn, S. M. (2018). Microeconomics: Principles, Problems, & Policies. Pearson.
  • Samuelson, P. A., & Nordhaus, W. D. (2010). Economics (19th ed.). McGraw-Hill Education.
  • Pindyck, R. S., & Rubinfeld, D. L. (2018). Microeconomics (9th Ed.). Pearson.
  • Varian, H. R. (2014). Intermediate Microeconomics: A Modern Approach. W.W. Norton & Company.
  • Perloff, J. M. (2017). Microeconomics (8th ed.). Pearson.
  • Baumol, W. J., & Blinder, A. S. (2015). Macroeconomics: Principles and Policy. Cengage Learning.
  • Frank, R. H., & Bernanke, B. S. (2018). Principles of Economics. McGraw-Hill Education.
  • Mankiw, N. G. (2017). Principles of Economics (8th ed.). Cengage Learning.
  • Hubbard, R. G., & O'Brien, A. P. (2018). Microeconomics. Pearson.
  • Friedman, M. (2002). Price Theory: A Provisional Text. University of Chicago Press.

Related Assignments