Let q f (p) be the demand function for a certain commodity, where q is the demand quantity and p the price of 1 unit We defined the elasticity of demand as (a) Find a differential equation satisfied by the demand function if the elasticity of demand is a linear function of price given by E( p) p 1 (b) Find the demand function in part (a), given f (1) 100 E(p) pf'(p) f(p)

Question: Let q = f (p) be the demand function for a certain commodity, where q is the demand quantity and p the price of 1

Let q = f (p) be the demand function for a certain commodity, where q is the demand quantity and p the price of 1 unit. We defined the elasticity of demand as E(p): -pf'(p) f(p)

(a) Find a differential equation satisfied by the demand function if the elasticity of demand is a linear function of price given by E( p) = p + 1.

(b) Find the demand function in part (a), given f (1) = 100.

E(p): -pf'(p) f(p)

Step by Step Solution

★★★★★

3.45 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Substitute Ep p 1 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Applied Calculus Questions!

The demand function for a certain commodity is p = 5 x/10. Find the consumer surplus when the sales level is 30. Illustrate by drawing the demand curve and identifying the consumer surplus as an...

The demand function for a certain product is q = -300p + 10,000. The fixed expenses are $500,000 and the variable expenses are $2 per item produced. a. Express the expense function in terms of q. b....

The demand function for a certain product is given by p= 500 + 1000 / q+1 Where p is the price and q is the number of units demanded. Find the average price as demand ranges from 49 to 99 units.

x ^ 2 + xy - y ^ 2 = 4 Find the slope of the tangent line at the point ( 2 , 2 ) . Then, find the equation of the tangent line at the point ( 2 , 2 ) . Suppose x = f ( p ) = 1 5 0 - 0 . 5 p 2 is the...

3.) Suppose that the demand equation for a certain commodity is q = 180 - p. (a.) Express the elasticity of demand as a function of p. (b.) Calculate the elasticity of demand when the price is p =...

Answer all questions correctly 1) For the years from 2002 and projected to 2024, the national health care Expenditures H, in billions of dollars, can be noticed by H= 1, 50De 0.053+ Where & is the...

Im having trouble understanding this problems, I need help figuring this out! 1. Solve the equation. Give your answer correct to 3 decimal places. 76 = 100 100 e0.07x 2. Solve the equation. Give your...

the demand function for a certain commodity is given by p = 100eq/2. (p is the price per unit and q is the number of units.) (a) At what price per unit will the quantity demanded equal 8 units?...

The demand function for a certain commodity is given by p 100e 9 2 p is the price per unit and q is the number of units a At what price per unit will the quantity demanded equal 4 units Round your...

The demand function for a certain commodity is given by p = 100 e q /2 . ( p is the price per unit and q is the number of units.) (A) At what price per unit will the quantity demanded equal 6 units?...

Inverse Laplace transform 1. F(s) = 3 / (s+3)^3 2. F(s) = 2s + 3 / s^2 + 3s + 2 3. F(s) = 3s - 2 / s^3 + 4s^2 + 4s + 1

S Company is an 80 percent owned subsidiary of P Corp. Excess at the time of acquisition only pertains to goodwill. The separate statements of comprehensive income of the two companies for 2011 are...

Question 6 0 ( 1 point ) ListenAccording to "What is FinTech - The RichTalk Series ( Part 1 ) , " which of the following is a Top Rated ( as per NPS ) FinTech Company? 1 ) IBM 2 ) Funding Circle 3 )...

Interest rates, part 2. In Exercise 39 you investigated the federal rate on 3-month Treasury bills between 1950 and 1980. The scatterplot below shows that the trend changed dramatically after 1980,...

The symbols and x both stand for means or averages but represent different quantities. Whats the difference between and x?

Why do the and x symbols in this chapter have subscripts? What do the subscripts represent?

Is the average of group averages always equal to the overall average? Lets make this question more precise: Suppose that an instructor teaches four sections of a course, and the average scores on an...

2 points Learning which has a long-term focus is referred to as Career enhancement Instruction Development O Training

A partial balance sheet for Captain D's Sportswear is shown below. (dollars in thousands) Assets: Cash Accounts receivable (net) Investments Inventory Prepaid rent Total current assets Property &...

TipTop Flight School offers flying lessons at a small municipal airport. The school's owner and manager has been attempting to evaluate performance and control costs using a variance report that...