### Given:- $ Q_d = 1100 - 2P $- $ Q_s = 3P - 100 $### 4. Arc ElasticityCalculate the arc elasticity where $ P = 250 $ and $ P = 200 $. **Explanation:**In economics, the demand equation $ Q_d = 1100 - 2P $ represents the quantity demanded as a function of price $ P $, where demand decreases as price increases.The supply equation $ Q_s = 3P - 100 $ represents the quantity supplied depending on the price, where supply increases as price rises.Arc elasticity is used to estimate the responsiveness of quantity demanded or supplied to changes in price over a specific range (between two price points, $ P = 250 $ and $ P = 200 $ in this case).**Steps to Calculate Arc Elasticity:**1. Determine the quantity demanded and supplied at both prices.2. Use the arc elasticity formula to find the elasticity value.This exercise illustrates how sensitive the supply and demand are to price changes, which is crucial for understanding market dynamics.

Answered: - (2)P Qd = 1100 Qs = 3P I. Given: %3D…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Question

### Given:

- $ Q_d = 1100 - 2P $
- $ Q_s = 3P - 100 $

### 4. Arc Elasticity

Calculate the arc elasticity where $ P = 250 $ and $ P = 200 $.

**Explanation:**

In economics, the demand equation $ Q_d = 1100 - 2P $ represents the quantity demanded as a function of price $ P $, where demand decreases as price increases.

The supply equation $ Q_s = 3P - 100 $ represents the quantity supplied depending on the price, where supply increases as price rises.

Arc elasticity is used to estimate the responsiveness of quantity demanded or supplied to changes in price over a specific range (between two price points, $ P = 250 $ and $ P = 200 $ in this case).

**Steps to Calculate Arc Elasticity:**

1. Determine the quantity demanded and supplied at both prices.
2. Use the arc elasticity formula to find the elasticity value.

This exercise illustrates how sensitive the supply and demand are to price changes, which is crucial for understanding market dynamics.

Expert Solution

Step 1

ANS

Elasticity is a measure that gives us an idea about how the quantity (Q) supplied or demanded of a commodity change when the price (P) of the commodity changes.

Mathematically;

$E l a s t i c i t y o f s u p p l y (E S) = \frac{% c h a n g e i n q u a n t i t y s u p p l i e d}{% c h a n g e i n p r i c e}$

$E l a s t i c i t y o f d e m a n d (E D) = \frac{% c h a n g e i n q u a n t i t y d e m a n d e d}{% c h a n g e i n p r i c e}$

Arc elasticity is given by the following formula:

$A r c E l a s t i c i t y = \frac{C h a n g e i n q u a n t i t y}{C h a n g e i n p r i c e} \times \frac{A v g . p r i c e}{A v g . Q u a n t i t y}$

For demand function:

When P = 250 then

$Q_{d} = 1100 - 2 P \Rightarrow Q_{d} = 1100 - 2 \times 250 \Rightarrow Q_{d} = 1100 - 500 = 600$

When P = 200 then

$Q_{d} = 1100 - 2 P \Rightarrow Q_{d} = 1100 - 2 \times 200 \Rightarrow Q_{d} = 1100 - 400 = 700$

Therefore when the price changed from $250 to $200 then the quantity demanded changes from 600 units to 700 units.

Thus change in price = $(250-200) = $50

And Change in quantity = 700-600 = 100 units

Average of price = (200+250)/2 = 225.

Average of quantity = (600+700)/2 = 650.

$\begin{array}{rcl} ∴ A r c E l a s t i c i t y o f d e m a n d & = & \frac{C h a n g e i n q u a n t i t y}{C h a n g e i n p r i c e} \times \frac{A v g . p r i c e}{A v g . Q u a n t i t y} \\ = & \frac{100}{50} \times \frac{225}{650} \\ = & 0.69 \end{array}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

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

Similar questions