Explanation Given: The demand function for a certain make of ten-speed bicycle is, p = − 0.001 x 2 + 250 The supply function or these bicycles is, p = 0.0006 x 2 + 0.02 x + 100 Formula used: The formula to calculate the consumer’s surplus is, C S = ∫ 0 x ¯ D ( x ) d x − p ¯ ⋅ x ¯ (1) Where, p ¯ is the unit market price, D ( x ) is the demand function and x ¯ is the quantity sold. The formula to calculate the producer’s surplus is, P S = p ¯ ⋅ x ¯ − ∫ 0 x ¯ S ( x ) d x (2) Where, p ¯ is the unit market price, S ( x ) is the supply function and x ¯ is the quantity supplied. Calculation: The given first function is, p = − 0.001 x 2 + 250 Second function is, p = 0.0006 x 2 + 0.02 x + 100 To plot the graph of given functions, follow the steps below. First press “ON” button on graphical calculator and press Y = key. Enter the right side of equations p = − 0.001 x 2 + 250 and p = 0.0006 x 2 + 0.02 x + 100 after the symbol Y 1 and Y 2 . Enter keystrokes ( − ) 0 . 0 0 1 X x 2 + 2 5 0 and 0 . 0 0 0 6 X x 2 + 0 . 0 2 X + 1 0 0 . The display will show the equations, Y 1 = − 0.001 X 2 + 250 Y 2 = 0.0006 X 2 + 0.02 X+100 Press the WINDOW key to change the window settings. X min = − 500 X max = 500 Xsc1 = 100 Y min = − 500 Y max = 500 Ysc1 = 100 Now, press the GRAPH key, produce the graph. Press the 2 nd key and then TRACE key, then press 5 key to select the intersect option. Move the cursor with the help of arrow key to the point where the graphs and press the ENTER key three times to get the intersection point as shown in figure below. Figure 1 The graph of given functions is shown in Figure 1. Hence, the equilibrium price is $ 160 and equilibrium quantity is $ 300 . Substitute 160 for p ¯ , 300 for x ¯ and − 0.001 x 2 + 250 for D ( x ) in equation (1) to calculate the consumer’s surplus. C S = ∫ 0 300 ( − 0.001 x 2 + 250 ) d x − ( 160 ) ( 300 ) = [ − 0.001 x 2 + 1 2 + 1 + 250 x ] 0 300 − 48000 [ ∵ ∫ a b x n d x = [ x n + 1 n + 1 ] a b ] = − ( 0

10th Edition

ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 6.7, Problem 1TE

To determine

To find: The consumer’s surplus and producer’s surplus by graphing utility.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.7, Problem 34E

Chapter 6.7, Problem 2TE

Chapter 6 Solutions

APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN

Ch. 6.1 - What is an antiderivative? Give an example.Ch. 6.1 - Prob. 2CQ Ch. 6.1 - What is the difference between an antiderivative...Ch. 6.1 - Prob. 4CQ Ch. 6.1 - In Exercises 1-4, verify directly that F is an...Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - In Exercises 1-4, verify directly that F is an...Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The consumer’s surplus and producer’s surplus by graphing utility.

Solution Summary: The author explains how to find the consumer's surplus by graphing utility. The supply function for a ten-speed bicycle is p=0.0006x2+0.02x+100.

Concept explainers

Videos

To find: The consumer’s surplus and producer’s surplus by graphing utility.

Want to see the full answer?

Chapter 6 Solutions