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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

The sum of consumer surplus and producer surplus is called the total surplus; it is one measure economists use as an indicator of the economic health of a society. Total surplus is maximized when the market for a good is in equilibrium.

  1. (a) The demand function for an electronics company’s car stereos is p(x) = 228.4 − 18 x and the supply function is ps(x) = 27x + 57.4, where x is measured in thousands. At what quantity is the market for the stereos in equilibrium?
  2. (b) Compute the maximum total surplus for the stereos.

(a)

To determine

To calculate: The equilibrium quantity of the stereos in the market.

Explanation

Given information:

The demand function for car stereos is p(x)=228.418x.

The supply function for car stereos is ps(x)=27x+57.4.

The function x is measured in thousands.

Calculation:

Consider p(x)=ps(x) (1)

Find the value of x using Equation (1).

Substitute 228.418x for p(x) and 27x+57.4 for ps(x) in Equation (1).

228

(b)

To determine

To calculate: The maximum total surplus for the stereos.

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