(A) Explanation Given: The price-demand and price-supply for the soybeans sales at a grain market is shown in the table. Calculation: Use online regression calculator to obtain the quadratic regression for the price- demand data is as shown below. From the above output, it is observed that the quadratic regression for the price demand equation is y = 0.000142857 x 2 − 0.0119143 x + 6.69857 . That is, D ( x ) = 0.000142857 x 2 − 0.0119143 x + 6.69857 . Use online regression calculator to obtain the linear regression for the price- supply data is as shown below. From the above output, it is observed that the linear regression for the price supply equation is y = 0.000114286 x 2 + 0.0000285714 x + 6.43286 . That is, S ( x ) = 0.000114286 x 2 + 0.0000285714 x + 6.43286 . Consider the price-demand equation D ( x ) = 0.000142857 x 2 − 0.0119143 x + 6.69857 and the price-supply equation S ( x ) = 0.000114286 x 2 + 0.0000285714 x + 6.43286 . For the equilibrium price p ¯ , the price-demand equation and the price-supply equation must be equal. That is, D ( x ) = S ( x ) 0.000142857 x 2 − 0.0119143 x + 6.69857 = 0.000114286 x 2 + 0.0000285714 x + 6.43286 ( 0 (B) To determine To find: The consumers’ surplus and the producers’ surplus and include a graph.

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 6.2, Problem 86E

(A)

To determine

To find: The equilibrium quantity and price.

(B)

To determine

To find: The consumers’ surplus and the producers’ surplus and include a graph.

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Chapter 6.2, Problem 85E

Chapter 6.3, Problem 1MP

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The equilibrium quantity and price.

Solution Summary: The equilibrium price is stackrelpapprox 6.5 and the equilibrium quantity is 23.578. The linear regression for the price-demand equation is as shown below.