Explanation Given information: 1 ) D ( x ) = ( x − 6 ) 2 , price in dollars per unit, that consumers are willing to pay for x units. 2 ) S ( x ) = x 2 + 12 , price in dollars per unit, that producers are willing to accept for x units. Formula used: Let p = S ( x ) be a supply function for a product. Then the producer surplus for Q units of the product, at a price per unit P , is calculated by the formula, P 0 = Q P − ∫ 0 Q S ( x ) ⋅ d x Here, P 0 is the producer surplus, Q is the number of units of the product, and P is the price per unit. The function expressed by the equation u ( x ) = x n is integrated with respect to x by using the following integral formula for algebraic function, ∫ u ( x ) d x = ∫ x n d x = | x n + 1 n + 1 | + c Here, c is the integration constant and n is a constant. The integration constant is not used for definite integrals. The definite integral of a function is calculated as, ∫ a b g ′ ( x ) = | g ( x ) | a b = g ( b ) − g ( a ) Here, g ′ ( x ) is the derivative of the function g ( x ) . Calculation: Consider the provided functions. 1 ) D ( x ) = ( x − 6 ) 2 2 ) S ( x ) = x 2 + 12 At equilibrium condition, equate the demand and supply functions. D ( x ) = S ( x ) . Substitute ( x − 6 ) 2 for D ( x ) and x 2 + 12 for S ( x ) . ( x − 6 ) 2 = x 2 + 12 Simplifying the equation, ( x − 6 ) 2 = x 2 + 12 x 2 + 36 − 12 x = x 2 + 12 36 − 12 = 12 x x = 2 Consider the function D ( x )

Pearson eText Calculus and Its Applications, Brief Edition -- Instant Access (Pearson+)

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Author: Marvin Bittinger, David Ellenbogen

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Chapter 5, Problem 17RE

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To calculate: The producer surplus at the equilibrium pointfor the functions D(x)=(x−6)2 and S(x)=x2+12.

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Chapter 5, Problem 16RE

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Chapter 5 Solutions

Pearson eText Calculus and Its Applications, Brief Edition -- Instant Access (Pearson+)

Ch. 5.1 - In Exercises 1-14, is the price, in dollars per...Ch. 5.1 - In Exercises 1-14, is the price, in dollars per...Ch. 5.1 - In Exercises 1-14, D(x) is the price, in dollars...Ch. 5.1 - In Exercises 1-14, is the price, in dollars per...Ch. 5.1 - In Exercises 1-14, D(x) is the price, in dollars...Ch. 5.1 - In Exercises 1-14, D(x) is the price, in dollars...Ch. 5.1 - In Exercises 1-14, D(x) is the price, in dollars...Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

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The producer surplus at the equilibrium pointfor the functions D ( x ) = ( x − 6 ) 2 and S ( x ) = x 2 + 12 .

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To calculate: The producer surplus at the equilibrium pointfor the functions D(x)=(x−6)2 and S(x)=x2+12.

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