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Get Full Access to First Course In Probability - 8 Edition - Chapter 7 - Problem 7.52
Get Full Access to First Course In Probability - 8 Edition - Chapter 7 - Problem 7.52

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# A population is made up of r disjoint subgroups.Let pi

ISBN: 9780136033134 163

## Solution for problem 7.52 Chapter 7

First Course in Probability | 8th Edition

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Problem 7.52

A population is made up of r disjoint subgroups.Let pi denote the proportion of the population thatis in subgroup i, i = 1, . . . , r. If the average weightof the members of subgroup i is wi, i = 1, . . . , r,what is the average weight of the members of thepopulation?

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PAM 2000 McDermott Spring 2016 April 5, 2016  simple economy: two consumers o market demand has to equal market supply o consumer A and consumer B both have a certain amount of good X and good Y that they can trade o build an Edgworth Box  given two graphs of the two consumers’ preferences, rotate one of them (consumer B)  corners  the bottom right corner: consumer A has all of good X and B has all of Y  top right: consumer B has all of both goods  dimensions  width: total supply of good X  height: total supply of good Y  their two indifference curves intersect  between the two points of intersection, both consumers are indifferent  points to which both consumers would be willing to trade to: between the two curves  “the eye of the economy”  randomly preset price  excess supply = too expensive  excess demand = too cheap  the length (or width) is the total supply so from the left (or bottom) is consumer A’s demand for X (or Y) and from the right (or the top) is consumer B’s demand for X (or Y) o if the demands don’t add up to precisely the supply then there is a surplus or shortage o equilibrium conditions:  1. quantity supplied=quantity demanded  in all markets  2. (when there is an interior solution and we have 2 consumers): (*as with Cobb-Douglas preferences) MRS1=MRS2  which =px/py  Pareto Optimality o equilibrium: there are no further possible gains from trade at that point o an allocation is pareto optimal if there is no other allocation which makes at least one agent better off without making any other agent worse off  pareto efficient  there are no more pareto improvements  moving to an allocation which makes at least one person better without harming anyone else o contract curve  the set of several pareto optimal allocations in an Edgworth Box  with linear preferences:  every point on the bottom and right axis (consumer A’s x axis and consumer B’s y axis) is pareto optimal  the contract curve is a backwards L formed by the two axes  First Welfare Theorem o any competitive equilibrium allocation will be pareto optimal April 7, 2016  externalities o externality: the direct effect of actions of a person or firm on another person’s wellbeing or a firm’s production capability rather than indirect effect through changes in prices o negative externality: one that harms o positive externality: one that benefits o externalities make competition inefficient r 450 e  private cost: cost of production only, excluding externalities a  social cost: private cost plus cost of the harms from externalities p A  social marginal cost (MC*): the cost of manufacturing one more o ton of paper to the paper firms plus the additional externality n es MC t ps 282 damage to people in the community from producing this last ton r B of papeC D p pc 240 H \$ 198 , G F MC g 84 p 30 0 Qs= 84 Qc= 105 225and Qo,ns of paper perad o deadweight loss: competitive market equates price with private marginal cost instead of social MC o competitive market: produces excessive negative externalities o optimal amount of pollution is greater than zero o government regulation on pollution  emissions fee: tax on air pollution  effluent charge: tax on discharges into the air or waterways  internalizing the externality: to bear the cost of the harm that one inflicts on others or to capture the benefit that one provides to others o monopoly  monopoly outcome (optimal quantity): may be less than the social optimum even with an externality  also could potentially be over-producing  because its decisions depend on its private marginal costs instead of social marginal costs  at the same time: monopoly tends to under-produce because it sets its price above its marginal cost o markets for pollution  cap and trade system: government gives firms permits each of which confers the right to create a certain amount of pollution  each firm may use its permits or sell them to other firms o public good: nonrival and nonexclusive  special type of externality  free riding: benefiting from the actions of others without paying

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