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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is a calculus question, not an economics question. Please use calculus/
Transcribed Image Text: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
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.
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