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#calculus #economics #mathematics

Constant slope does not imply constant elasticity. To see this, consider the linear demand function Q=a-bP, which has constanst slope equal -b. But the elasticity implied by this demand function is E=(dQ/dP)(P/Q)=-b(P/Q). Since the ratio P/Q gets smaller and smaller as Q increases, demand is more leastic at high prices and less elastic at low prices.

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**Elasticity vs. Slope?**

Best Answer helper answered 5 years ago <span>Constant slope does not imply constant elasticity. To see this, consider the linear demand function Q=a-bP, which has constanst slope equal -b. But the elasticity implied by this demand function is E=(dQ/dP)(P/Q)=-b(P/Q). Since the ratio P/Q gets smaller and smaller as Q increases, demand is more leastic at high prices and less elastic at low prices. This makes intuitive sense, since it is reasonable that quantity demanded is more sensitive at high prices than it is at low prices. A demand function of the form Q=b/P is called a constant elasticity demand function. To see this, note that E=(dQ/dP)(P/Q)=(-b/P^2)(P/Q)=(-b/P^2)(P/... a constant. More generally, if

Best Answer helper answered 5 years ago <span>Constant slope does not imply constant elasticity. To see this, consider the linear demand function Q=a-bP, which has constanst slope equal -b. But the elasticity implied by this demand function is E=(dQ/dP)(P/Q)=-b(P/Q). Since the ratio P/Q gets smaller and smaller as Q increases, demand is more leastic at high prices and less elastic at low prices. This makes intuitive sense, since it is reasonable that quantity demanded is more sensitive at high prices than it is at low prices. A demand function of the form Q=b/P is called a constant elasticity demand function. To see this, note that E=(dQ/dP)(P/Q)=(-b/P^2)(P/Q)=(-b/P^2)(P/... a constant. More generally, if

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posted by: PiotrWasik

all users in topic: PiotrWasik

all tags in topic: calculus economics mathematics

first message: 13:18, Sunday, August 10, 2014

last message: 13:18, Sunday, August 10, 2014

messages count: 1

Wiki says *"This makes intuitive sense, since it is reasonable that quantity demanded is more sensitive at high prices than it is at low prices."* - not true, it is a simple fact that relative values (elasticity) change differently than absolute values (slope).