### Understanding Supply and its Rate of Change with Respect to PriceTo find the supply $ S(p) $ and the instantaneous rate of change of supply with respect to price when the price is 40 dollars, the following problem is presented:\[ S(p) = \frac{100p}{0.7p + 3} \]where $ p $ is the price in dollars.1. **Calculate the Supply at $ p = 40 $ Dollars** \[ S(40) = \_\_\_\_\_ \text{ players} \]2. **Calculate the Instantaneous Rate of Change of Supply with Respect to Price at $ p = 40 $ Dollars** \[ S'(40) = \_\_\_\_\_ \text{ players/dollar} \]3. **Estimate the Increase in Supply if the Price Rises from $ p = 40 $ to $ p = 50 $ Dollars** Use your answers from parts 1 and 2 to estimate the increase in supply. Round your answer to the nearest integer. \[ \text{Supply increase} \approx \_\_\_\_\_ \text{ players} \]This exercise helps in understanding how changes in price can impact supply, an important concept in economic theory.### Explanation of the Procedure and EstimationsTo solve the problem step by step:- **Step 1: Calculate $ S(40) $** Substitute $ p = 40 $ into the supply function: \[ S(40) = \frac{100 \times 40}{0.7 \times 40 + 3} = \frac{4000}{28 + 3} = \frac{4000}{31} \] Solve to get the supply at 40 dollars.- **Step 2: Calculate $ S'(40) $** Differentiate $ S(p) $ with respect to $ p $ to find $ S'(p) $. This involves applying the quotient rule of differentiation. Then, substitute $ p = 40 $ into $ S'(p) $.- **Step 3: Estimate Increase in Supply** Using the derivative $ S'(p) $ at $ p = 40 $, estimate the increase in supply when the price increases from 40 to 50 dollars with the following approximation: \[ \text

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100p 0.7p + 3 S(p) = Find the supply and the instantaneous rate of change of the supply with respect to price when the price is 40 dollars. S(40)| = players s'(40)|= players/dollar Use your previous answers to estimate the increase in supply if the price rises from 40 to 50 dollars. Round your answer to the nearest integer. Supply increase | players

100p 0.7p + 3 S(p) = Find the supply and the instantaneous rate of change of the supply with respect to price when the price is 40 dollars. S(40)| = players s'(40)|= players/dollar Use your previous answers to estimate the increase in supply if the price rises from 40 to 50 dollars. Round your answer to the nearest integer. Supply increase | players

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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