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1- Suppose you have been hired as an economic consultant concerning the world demand for oil. The demand function is q = D(x) = 35,000 + 150x - 4x², for 0≤x≤ 180 where q is measured in millions of barrels of oil per day at a price of x dollars per barrel. D(x) = -4x² +150x + 35,000 = D'(x) = -8x +150 a. Find the elasticity. E(x) = -x (-8x+150) -4x² +150x+35,000 b. Find the elasticity at a price of $45 per barrel, stating whether demand is elastic or inelastic at that price. 189 673 E(45)= E(45) <1⇒ inelastic 0.281 c. Find the elasticity at a price of $60 per barrel, stating whether demand is elastic or inelastic at that price. E(60) = 99 148 ~ 0.67 E(75) = 21~1,42 19. e. At what price is revenue a maximum? -X(-8x+150) -4x² +150x+35,000 E (60) <1 ⇒ inelastic d. Find the elasticity at a price of $75 per barrel, stating whether demand is elastic of inelastic at that price. E(75) >1 → elastic

1- Suppose you have been hired as an economic consultant concerning the world demand for oil. The demand function is q = D(x) = 35,000 + 150x - 4x², for 0≤x≤ 180 where q is measured in millions of barrels of oil per day at a price of x dollars per barrel. D(x) = -4x² +150x + 35,000 = D'(x) = -8x +150 a. Find the elasticity. E(x) = -x (-8x+150) -4x² +150x+35,000 b. Find the elasticity at a price of $45 per barrel, stating whether demand is elastic or inelastic at that price. 189 673 E(45)= E(45) <1⇒ inelastic 0.281 c. Find the elasticity at a price of $60 per barrel, stating whether demand is elastic or inelastic at that price. E(60) = 99 148 ~ 0.67 E(75) = 21~1,42 19. e. At what price is revenue a maximum? -X(-8x+150) -4x² +150x+35,000 E (60) <1 ⇒ inelastic d. Find the elasticity at a price of $75 per barrel, stating whether demand is elastic of inelastic at that price. E(75) >1 → elastic

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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MTH1073 Class Activity Name: Brian Hazelwood Suppose you have been hired as an economic consultant concerning the world demand for oil. The demand function is q = D(x) = 35,000 + 150x - 4x², for 0 ≤ x ≤ 180 where q is measured in millions of barrels of oil per day at a price of x dollars per barrel. D(x) = -4x² +150x + 35,000 D'(x) = -8x +150 a. Find the elasticity. E(x) = -x (-8x+150) -4x² +150x+35,000 b. Find the elasticity at a price of $45 per barrel, stating whether demand is elastic or inelastic at that price. 189 E(45)= E(45) <1⇒ inelastic 673 ~ 0.281 c. Find the elasticity at a price of $60 per barrel, stating whether demand is elastic or inelastic at that price. E(60) = 99 10/25/2022 E (60) <1 ⇒ inelastic. d. Find the elasticity at a price of $75 per barrel, stating whether demand is elastic of inelastic at that price. E(75) >1⇒ elastic 148 ~ 0.67 E (75) = 20 ~ 1,42 19. e. At what price is revenue a maximum? -X(-8x+150) -4x² +150x+35,000 f. What quantity of oil will be sold at the price that maximizes revenue? Compare the current world price to your answer. g. In August 2017, a barrel of crude oil was selling for about $48. At this price, will a small increase in price cause total revenue to increase or decrease?
Transcribed Image Text:MTH1073 Class Activity Name: Brian Hazelwood Suppose you have been hired as an economic consultant concerning the world demand for oil. The demand function is q = D(x) = 35,000 + 150x - 4x², for 0 ≤ x ≤ 180 where q is measured in millions of barrels of oil per day at a price of x dollars per barrel. D(x) = -4x² +150x + 35,000 D'(x) = -8x +150 a. Find the elasticity. E(x) = -x (-8x+150) -4x² +150x+35,000 b. Find the elasticity at a price of $45 per barrel, stating whether demand is elastic or inelastic at that price. 189 E(45)= E(45) <1⇒ inelastic 673 ~ 0.281 c. Find the elasticity at a price of $60 per barrel, stating whether demand is elastic or inelastic at that price. E(60) = 99 10/25/2022 E (60) <1 ⇒ inelastic. d. Find the elasticity at a price of $75 per barrel, stating whether demand is elastic of inelastic at that price. E(75) >1⇒ elastic 148 ~ 0.67 E (75) = 20 ~ 1,42 19. e. At what price is revenue a maximum? -X(-8x+150) -4x² +150x+35,000 f. What quantity of oil will be sold at the price that maximizes revenue? Compare the current world price to your answer. g. In August 2017, a barrel of crude oil was selling for about $48. At this price, will a small increase in price cause total revenue to increase or decrease?
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