Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q8. (page 85)

In Example 2.8 we examined the effect of a 20-percent decline in copper demand on the price of copper, using the linear supply and demand curves developed in Section 2.6. Suppose the long-run price elasticity of copper demand were -0.75 instead of -0.5.

  1. Assuming, as before, that the equilibrium price and quantity are P_ = $3 per pound and Q_ = 18 million metric tons per year, derive the linear demand curve consistent with the smaller elasticity.

  2. Using this demand curve, recalculate the effect of a 55-percent decline in copper demand on the price of copper.

Short Answer

Expert verified

  1. The demand curve will be Q = 31.5 – 4.5P.

  2. The demand falls by 55% then price fall by 30%.

Step by step solution

01

Explanation for part (a)

Let the demand curve be Q = a + bP. The coefficient of P is the change in quantity demand by a change in price; the value of a is the intercept of the demand curve.

The elasticity of demand will be:

ED=△Q△P×PQED=-0.75-0.75=△Q△P×318△Q△P=-0.75×183b=-4.5

The intercept value is calculated below:

18 = a - 4.5(3)

a = 18 + 13.5

a = 30.5

The demand curve will be Q = 31.5 – 4.5P.

02

Explanation for part (b)

The demand curve falls by 55%; thus, the new demand curve will be:

QD'=0.45QD=0.45(31.5-4.5P)=14.18-2.03PThesupplycurveisQ=-9+9PAtequilibrium,D=S14.18-2.03P=-9+9P2.03P+9P=14.18+911.03P=23.18P=2.10

The demand falls by 55%, then the price fall by 30%2.1-33×100=30%

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let’s think about the market for air travel. From August 2014 to January 2015, the price of jet fuel increased

roughly 47%. Using the four-step analysis, how do you think this fuel price increase affected the equilibrium price

and quantity of air travel?

Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:

PRICE

(DOLLARS)

DEMAND

(MILLIONS)

SUPPLY

(MILLIONS)

602214
802016
1001818
1201620

a. Calculate the price elasticity of demand when the price is \(80 and when the price is \)100.

b. Calculate the price elasticity of supply when the price is \(80 and when the price is \)100.

c. What are the equilibrium price and quantity?

d. Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how large will it be?
  1. In Example 2.8 (page 74), we discussed the recent decline in world demand for copper, due in part to China’s decreasing consumption. What would happen, however, if China’s demand were increasing?

  2. Using the original elasticities of demand and supply (i.e., ES = 1.5 and ED = -0.5), calculate the effect of a 20-percent increase in copper demand on the price of copper.

  3. Now calculate the effect of this increase in demand on the equilibrium quantity, Q*.

  4. As we discussed in Example 2.8, the U.S. production of copper declined between 2000 and 2003. Calculate the effect on the equilibrium price and quantity of both a 20-percent increase in copper demand(as you just did in part a) and of a 20-percent decline in copper supply.

Does a price ceiling change the equilibrium price?

Example 2.9 (page 76) analyzes the world oil market. Using the data given in that example:

a. Show that the short-run demand and competitive supply curves are indeed given by

D = 36.75 - 0.035P

SC= 21.85 + 0.023P

b. Show that the long-run demand and competitive supply curves are indeed given by

D = 45.5 - 0.210P

SC= 16.1 + 0.138P

c. In Example 2.9 we examined the impact on price of a disruption of oil from Saudi Arabia. Suppose that instead of a decline in supply, OPEC production increases by 2 billion barrels per year (bb/yr) because the Saudis open large new oil fields. Calculate the effect of this increase in production on the price of oil in both the short run and the long run.
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free