The price-demand equation, D(x), and the price-supply equation, S(x), of a Slow Cooker are given below. k - x p = D(x) and p =s(x) = 0.25x2 + 7, for some constant k. 4 %3D %3D When the price is pegged at $15, the consumers' surplus is found to be $200. (a) Find k. (You will be able to solve for two values of k. Provide an explanation why one of these values is not feasible.) (b) Find the equilibrium price and equilibrium quantity using the value of k found in part (a). (c) Find the consumers' surplus at the equilibrium point. Interpret what this value represents. (d) Find the producers' surplus at the equilibrium point. Interpret what this value represents.

The price-demand equation, D(x), and the price-supply equation, S(x), of a Slow Cooker are given below. k - x p = D(x) and p =s(x) = 0.25x2 + 7, for some constant k. 4 %3D %3D When the price is pegged at $15, the consumers' surplus is found to be $200. (a) Find k. (You will be able to solve for two values of k. Provide an explanation why one of these values is not feasible.) (b) Find the equilibrium price and equilibrium quantity using the value of k found in part (a). (c) Find the consumers' surplus at the equilibrium point. Interpret what this value represents. (d) Find the producers' surplus at the equilibrium point. Interpret what this value represents.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section4.2: Modeling With Linear Functions

Problem 51SE: The Federal Helium Reserve held about 16 billioncubic feet of helium in 2010 and is being depleted...

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