For most products, higher prices result in a decreased demand, whereas lower pri
ID: 3064101 • Letter: F
Question
For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand. Let
d = annual demand for a product in units
p = price per unit
Assume that a firm accepts the following price-demand relationship as being realistic:
d = 800 - 10p
where p must be between $20 and $70.
How many units can the firm sell at the $20 per-unit price? Round your answer to the nearest whole number.
d = units
At the $70 per-unit price? Round your answer to the nearest whole number.
d = units
What happens to annual units demanded for the product if the fim increases the per unit price from $26 to $27?
If the firm increases the per unit price from $26 to $27, the number of units the firm can sell by .
From $42 to $43?
If the firm increases the per unit price from $42 to $43, the number of units the firm can sell by .
What is the suggested relationship between the per-unit price and annual demand for the product in units?
This suggests that the relationship between the per-unit price and annual demand for the product in units is between $20 and $70 and that annual demand for the product by units when the price is increased by $1.
Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price. Express your answer in terms of p.
TR =
Based on other considerations, the firm’s management will only consider price alternatives of $30, $40, and $50. Use your model from part (c) to determine the price alternative that will maximize the total revenue.
Total revenue is maximized at the $ price.
What are the expected annual demand and the total revenue corresponding to your recommended price?
Round your answer to the nearest whole number.
d = units
Round your answer to the nearest dollar.
TR = $
Explanation / Answer
At $20, D=800-10p=800-10*20=600
At $70, D=800-10p=800-10*70=100
If the firm increases the per unit price from $26 to $27,
D= 800-10p= 800-10*26 = 540
D= 800-10p= 800-10*27 = 530
The number of units the firm can sell reduces by 10 units from 540 to 530
If the firm increases the per unit price from $42 to $43,
D= 800-10p= 800-10*42 = 380
D= 800-10p= 800-10*43 = 370
The number of units the firm can sell reduces by 10 units from 380 to 370
A single unit increase in the price will lead to reduction in quantity demanded by 10 units.
Mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price. Express your answer in terms of p.
D=800-10p or TR = D*p =(800-10p)*p = 800p-10p^2
At $30,
TR=800*30-10*302=15,000
At $40, TR=800*40-10*402=16,000
At $50, TR=800*50-10*502=15,000
Therefore maximum Total Revenue is maximized at a price of $40.
At the Price of $40, the expected annual demand is
D=800-10*40=400 and
total revenue will be equal to = 400*40 = $16,000
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