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Special Study for Honors Candidates in Music

by: Guadalupe Rodriguez

Special Study for Honors Candidates in Music MUSIC H195

Marketplace > University of California - Berkeley > Music > MUSIC H195 > Special Study for Honors Candidates in Music
Guadalupe Rodriguez

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This 15 page Class Notes was uploaded by Guadalupe Rodriguez on Thursday October 22, 2015. The Class Notes belongs to MUSIC H195 at University of California - Berkeley taught by Staff in Fall. Since its upload, it has received 49 views. For similar materials see /class/226552/music-h195-university-of-california-berkeley in Music at University of California - Berkeley.


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Date Created: 10/22/15
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Private Goods Are Summed Horizontally Exclusive once you buy it you own it and can consume it as you please Rival a good taken off the shelf it isn t there for other people to consume We sum private goods horizontally because consumers cannot consume the same units Rivalry in consumption is what makes the market pricing system so incredibly effective and why the invisible hand hypothesis can work A price is a per unit charge for a good so that when goods are consumed away due to a rivalry between consumers supply shortages will tend to correct the market by driving up prices as consumers compete for the few remaining goods Similarly a supply surplus will cause firms to lower the price of the good until an equilibrium is met that will clear the market Public goods however cannot be so easily and efficiently priced Figure 72 Deriving Aggregate Demand for Public Good P111161 P D1 Qll39nax Q 1 F211an QEInaX Q P 11mm P21dax 3 3211122 Q Aggregate demand in the economy for a public good is the vertical sum of individual demand curves Demand is summed vertically because all individuals can enjoy the same Therefore for each marginal unit of water quality aggregate demand the sum of individual value for the unit Almost no good or service is completely nonrival On the other hand many goods are not completely rival either Hence nonrivalry as a characteristic of a public good is a relative not an absolute concept However for the purpose of discussion we often use the notion of a pure public good A number of environmental amenities have public good characteristics For example we will discuss the socially optimal level of provision of regional air quality a relatively pure public good We will also discuss nonuse values which are types of environmental bene ts that are also public goods Many environmental issues can be thought of in terms of public goods For example the reason the Coase Theorem may not work can be thought of in terms of public goods if air and water resources were private goods they could be traded ef ciently in a market We will now show why inef ciencies can arise in the provision of public goods Heterogeneity Non Rivalry and Market Failure Consider Two Goods with Identical Aggregate Demand The rst good is a private good ie Chicken Sandwiches The second good is a public good ie Water Quality at Mono Lake Figure 73 PRIVATE GOOD PUBLIC GOOD Q2 Q Q1 Q2 Q Q1Q2 Quantity Quantity Private Good Notice that the market price is an ef cient mechanism The equilibrium price of a chicken sandwich is PMC so that each chicken sandwich costs P Consumers compete for the consumption of sandwiches and at a price of P will selfselect socially optimal quantities Consumer l eats Ql sandwiches consumer 2 eats Q2 sandwiches and Q1 Q2 Q the aggregate efficient level The shaded regions show the total payment by each individual Public Good Notice that the market price is no longer an efficient mechanism because the stock of a public good is never consumed away The equilibrium price of water quality cannot be PMC because then Consumer 1 would not pay for any water quality improvements Consumer 2 would pay for only Q2 and since Q2 lt Q the efficient level of water quality would not be met To see what we would like to do note the analogy to the case of the private good recognizing that public goods are the mirror image Thus the social optimal solution would be to provide Q and then charge each consumer a unit price equal to the individuals marginal value at Q or P1 and P2 As in the case of private goods the high demand individual will pay a larger amount than the individual with a lower willingness to pay for the good shown as the shaded regions Yet such a solution may not be possible The reason inef ciency arises in providing public goods is that unlike price quantity is not an effective market mechanism For a given quantity individuals will not automatically selfselect their optimal price but will instead wish to pay the lowest price possible when they cannot be excluded from consuming the good Non Excludability and Market Failure Public goods are a special concern to economists because there can be quotmarket failurequot in the private market provision of both pure and impure public goods The primary cause of market failure involving public goods is nonexcludability Non excludability means that the producer of a public good cannot prevent individuals from consuming it Non excludability is a relative not an absolute characteristic of most public goods A good is usually termed non excludable if the costs of excluding individuals from consuming the good are very high Private markets often under provide non excludable public goods because individuals have the incentive to free ride or to not pay for the benefits they receive from consuming the public good With a free rider problem private firms cannot earn suf cient revenues from selling the public good to induce them to produce the socially optimal level of the public good Flgul39e 7 4 Market Failure X1 x4 anx x D Demand ofone lndlvldual for publlc good x D2 Total Demand oftwo lndlvldunls for publlc good x D3 Tolel Demand ofthree lndlvlduals for pub be good x Du four lndlvlduals forpubllc good x T MC Marglnalcost ofprovldlng thepubllc goodx The soclally olemal level of pub be good x wlth four consumers 15 x4 Note LhaLLhe nhmal lulul mum ll c v A v v r nucl yll m nle l n end Inthls a u publlc good becauseno one lsvvllllnglo purchase It Forexnmple If lndlvldual l decldes V l loune olemal level ofprovlslon othe publlc good x4 Optimal Pruvlsmn with Humngm us Indlvl uzls x level ofprovlslon ofa publlc good nnumberofhomogmeous lndlvlduals n a soelely lnvzrxz zde ofone lndlvldual DX DXa e bX Invase demand ofn homogeneous Individuals laggegale demand nDX na bX na an gt nTBX f nDX dX Inverse Supply MCX c d X gt TCX f MCX dX The socially optimal level of provision of X occurs where nTBX TCX is maximized which is given by the solution to the problem X X ngWX anxdx fMCxdx 0 0 The FOC for this problem is nDX MCX or na an c dX Solving the FOC for X na c X nbd Note that as n becomes very large X approaches the value ab which is the X intercept of aggregate demand draw a little supplydemand graph and see how the intersection of supply and demand causes the optimal level of X to approach the value of ab as the n becomes very large For public goods the X intercept of aggregate demand is the level of provision of the public good at which the marginal bene t to any individual of providing an additional unit of the public good is zero Numerical Example Supposea10blc0andd5 This gives us nDX n10 7 X and MCX 5X Examine what happens to X as n increases n 1 gt DX 10 1X DX MCX gt Xnl 166 n 5 gt 5DX 50 5X DX MCX gt Xn5 5 n 10 gt 10DX 100 10X DX MCX gt Xn10 666 n 100 gt 100DX 1000 100x DX MCX gt Xn100 95 Private Market Outcome for a Non excludable Public Good Private providers will provide public goods up to the point where the marginal bene t of one individual the other individuals free ride equals the marginal cost of providing the public good The individual takes other agents behavior as given xed and solves the following problem X Max fDix E Djxdx TCX X 0 jsi ltgt X X MaxfDixdx fMCxdx X 0 0 with FOC DiXMCX or abXcdX Solving for the level of the public good provided by a private market d C bd X Camp Comparing X m p with X we nd that X m p lt X Hence the private market under provides the public good Other Mechanisms for Providing the Socially Optimal Level of Public Goods In those cases where the private market fails to provide the efficient level of public goods provision of public goods requires collective action People need to realize that a public goods situation exists and either raise contributions from private individuals to fund the public good or let the government provide the public good Mechanisms to provide public goods include 1 Civic responsibility individual volunteerism private fund raising and donation Examples donations to the Arts for symphony halls volunteer re departments nature reserves nanced by groups such as the Nature Conservatory 2 Private provision of excludable public goods Examples movies music concerts 3 Public provision of excludable public goods through the use of entrance fees Example entrance fees for a National Park 7 4 Public rovision of non excludable ublic oods throu h the use of eneral P P g g g government tax revenues Example taxes earmarked for National Defense 5 Religious beliefs Examples church services are a public good during the ceremony a basket is passed around for collections Religion can prevent free riding by convincing people that God is watching The Relationship Between Wealth and Public Good Provision One of the bene cial aspects of an unequal income distribution is that some rich people have the ability to nance public goods through donation volunteering and charity Of course this is not necessarily what happens In order for voluntary donation to occur members of society especially rich individuals need to have community spirit and a sense of moral obligation which they may lack However there are many historical examples where the rich have nanced the provision of public goods Music and the Arts were nanced by kings and knights The rich educated themselvesicollected books and preserved knowledge The rich can buy expensive early versions of new products hence generating incentives for RampD oriented towards innovation due to larger monetary incentives The Church introduced mechanisms for public goods provision Monks nuns priests serve as a quotpublic goodquot Religious beliefs provided incentives to public good provisions Education Government Provision of NonExclndable Public Goods T hrongh Taxes The government can correct market failure and provide the socially optimal level of a public good by nancing the provision of public goods with tax revenue Public nancing of public goods may be the only option in cases where the public good is non excludable and therefore entry fees cannot be charged we cover the entry fee case later In fact one could argue that the only role for government in a society is to provide non excludable public goods such as National Defense and Social Welfare Programs The Speci cation of Congestion Costs in Public Goods Models Of course most public goods are not pure public goods For example although roads are used simultaneously by many people and are public goods an increasing number of users can reduce the bene ts to each individual due to congestion costs Congestion costs or negative congestion extemalities are a type of extemality that can occur with public goods Congestion costs can be a problem for several environmental amenities and natural resources For example the bene ts to each viewer of a scenic vista may be reduced if the overlook site becomes crowded Similarly if too many shing E boats crowd together over a school of sh then the costs to each sherman of catching the sh may increase due to accidental collisions inef ciently short trawling runs nets damaged by other boats propellers etc However congestion can also create bene ts in some cases Positive congestion extemalities occur often in the provision of information networks For example consider the information highway When the rst individual subscribed to email the value of the service was equal to zero since there was no one out there to send messages to As subscription to the service increased however the value of email increased due to the positive congestion extemality In an economic model the existence of a negative congestion extemality means that the bene t each individual gains from consuming a public good decreases with the number of individuals consuming the public good For example if X is the level of provision of a public good N is the number of people consuming the public good and BiXN is the bene t to an individual associated with consuming a public good at a level of X when N individuals are using the public good then the existence of congestion costs implies that dBidN lt 0 that is the bene t to an individual of consuming the public good decreases as the number of individuals consuming the public good increases Note the contrast to a pure public good where dBidN0 due to nonrivalry Hence when building an economic model involving congestible public goods the functional form we choose to represent the bene ts to an individual of consuming a public good should have the property that the bene ts to an individual decrease as the number of individuals consuming the public good increases For example consider the following functional form for the bene ts to an individual of consuming a congestible public good 2 BiXNabX CX where the parameters abc gt 0 When we maximize bene ts with respect to N we find that abX cX2 dN N2 Since the expression is negative this implies a negative congestion extemality But what about the shing example where we noted that congestion led to increased costs rather than to decreased bene ts If we simply rede ne the bene ts from fishing as the net bene ts or pro ts from shing then we can note that the profits 9 from shing decrease as the costs of shing increase and dBidN lt 0 would still be a necessary condition for the presence of congestion costs Incandescence 10 We used MAX MSP software to create a exible program to musically sonify multiple data sets using many changeable parameters Here is a summary of what the resulting software does Allows user to choose a data set Interpolates over missing data Normalizes data bins so values in each bin can be comparable currently six bins are available Maps the time variable in the data to a shorter or longer time Provides three ways to map the six data bins to music using gt a filter gt a resonance gt a probability type of quotmachine The filter and resonance interpreters maps particle energy flux into frequency as it will be explained below Probability type of machine In this approach we choose a different and less direct mapping shown in resonators and filters by using algorithmic procedures and maintain the same dramatic expression shown in the other models The data is mapped to piano notes where a Gaussian function determines dynamics an exponential determines the note rate and a Beta function defines the pitches SEP data is divided in 45 steps and triggers it every 125 seconds The duration of each event have a correspondence with bin no 1 with events that should last from 3 to 9 seconds The 2nd bin triggers the exponential function defining the note rate Bin no 3 controls the interval distance between each note produced beta function Bin no 4 regulates the band with of a gaussian distribution function defining the intensity of each note produced Bins 5 and 6 work together in the following way Bin no 5 defines the register in the piano where the lower note should occur for each event and bin no 6 defines the octave range starting in the note defined in bin no 5 Quick start To explore this sound engine with other SEP data click on the bang object fig 1a located in the top left corner and surf in your computer for SEP data files Load data from incandescence fig 1a 1 Turn on the audio in your computer by clicking the start audio button down center fig 1b 2 Drag the mouse in the ubumenu located in Span of sonification top right where it says 30 seconds Span of sonification I 0 seconds fig 2a Once released you will start listening to resonators interpretation for 30 seconds with fixed frequencies and volume configurations For a manual scanning of the data use the slider in the top left fig 2b 3 For listening to the filters go to the area next to the audio buttons and drag the mouse in the orange ubumenu box low center area and choose wind fig 3 Go back to Span of sonification and listen to the wind reson filters L R ch ch2 fig 3 4 To listen to the piano click on the blue right low button fig 4a The application will pop up a window fig 4b illustrating the graphic evolution of the functions used to generate rhythrn pitch and loudness for each of the notes generated while you are listening When the sequence in over this window will disappear a few seconds later Linear 12 tone scale fig 4a current event rgt g4b The probability model has an option for choosing 3 types of scales chromatic 12 tone scale diatonic white keys of the piano and pentatonic black keys of the piano Contained in the lowest ubumenu in the purple area Exploring new sounds with the same data Incandescence permits to configure the correspondence in bins and frequency range in resonators and filters while listening via the range sliders fig 5 The minimum and maximum values can be set by dragging with the mouse across a range in the range slider fig 5 The volume for each bin is controlled manually through the multi slider objects situated in the center of the window also by dragging and navigating with the mouse inside the object fig 6 resonators volume for each bin 1 2 3 4 5 6 fig 6 To experiment with new durations go to the Span of sonification fig 2a area and type in the number box any amount in seconds The program is able to interpolate or not the data coming from SEP The purpose in interpolating the data is to make smoother the transitions between abrupt changes caused by absent data The 3 interpolation modes used for this purpose are linear lagrange 2 and lagrange 3 Each sonification process can have its own interpolation mode Contained in the brown blue and purple areas Dragging the mouse in the grey ubumenu box will pop up the menu with the interpolation functions The fig 7 choose then the correspondence interpolation function for each process Lagrange 3 fig 7 For additional graphic illustration of data the user can pop up two additional windows by clicking any of the two low buttons situated in the left low corner of the application fig 8 lt no display i9 L lt range of frequencies for sonification 39LJ lt origina data With the intrpolation function fig 8 Listening to 2 or more processes simultaneously To hear resonators and filters simultaneously drag the mouse in the orange ubumenu box low center area and choose resonators wind reson filters L R L R chi ch2 fig 9 You are also able to combine manually the channel assignments of the outputs by clicking in the red buttons To hear the piano too click into the blue button while the process is going on in resonators and filters


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