2. In the following market model, p is price, qº is quantity demanded and qs is quantitysupplied:9=3-2p.and9³ = -1 + 4p.Suppose that the market does not clear instantaneously, but that price increases whenthere is excess demand and decreases when there is excess supply:p = ½ (9² - 9³),where p(b)Write out a first-order differential equation of p.

Given: qD=3-2pandqS=-1+4p p˙=12qD-qS, where p˙≡dpdt. We have to write a first-order differential…

Answered: . In the following market model, p is…

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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Suppose the Consumer Price Index. (CPI), can be modeled by the following equation between the years 2000 and 2019: CPI(1) = 200 – 10te – 100e 0
b. Find the equilibrium quantity.
(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
A certain gas reserve held about 27 billion cubic feet of the gas in 2010 and is being depleted by about 1.7 billion cubic feet each year. (a) Give a linear equation for the remaining gas reserves, R, in terms of t, the number of years since 2010. (Let R be measured in billions of cubic feet.) R(t) = (b) In 2015, what will the gas reserves be? (Round your answer to one decimal place.) billion ft3(c) If the rate of depletion doesn't change, in what year will the gas reserve be depleted? (Round your answer down to the nearest year.)
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. D(x) = e X+2 S(x) = e x-6 a) Find the equilibrium point. b) Find the consumer surplus at the equilibrium point. c) Find the producer surplus at the equilibrium point. a) What are the coordinates of the equilibrium point? (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Do not include the $ symbol in your answer)

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