MMEsupplydemandsoln

MMEsupplydemandsoln - 2011 - Steven Tschantz Supply and...

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© 2011 - Steven Tschantz Supply and Demand Steven Tschantz 1/25/11 Exercises Complete the following exercises. You can save a copy of this notebook, delete the material above, insert and evaluate your commands computing answers below, save your results, and email your final version to tschantz@math.vanderbilt.edu ± Original program In[1]:= demandform @ p_ D = demandslope * p + demandintercept Out[1]= demandintercept + demandslope p In[2]:= population = 10 000; In[3]:= demandconditions = 8 demandform @ 50. D ± 0.20 * population, demandform @ 40. D ± 0.25 * population < Out[3]= 8 demandintercept + 50. demandslope ± 2000., demandintercept + 40. demandslope ± 2500. < In[4]:= demandsolns = Solve @ demandconditions, 8 demandslope, demandintercept <D Out[4]= 88 demandslope fi - 50., demandintercept 4500. << In[5]:= demand @ p_ D = demandform @ p D ± . demandsolns @@ 1 DD Out[5]= 4500. - 50. p In[6]:= supplyform @ p_ D = supplyslope * p + supplyintercept Out[6]= supplyintercept + p supplyslope In[7]:= supplyconditions = 8 supplyform @ 40. D ± 2100., supplyform @ 50. D ± 2300. < Out[7]= 8 supplyintercept + 40. supplyslope ± 2100., supplyintercept + 50. supplyslope ± 2300. < In[8]:= supplysolns = Solve @ supplyconditions, 8 supplyslope, supplyintercept <D Out[8]= 88 supplyslope 20., supplyintercept 1300. << In[9]:= supply @ p_ D = supplyform @ p D ± . supplysolns @@ 1 DD Out[9]= 1300. + 20. p In[10]:= marketcondition = demand @ p D ± supply @ p D Out[10]= 4500. - 50. p ± 1300. + 20. p
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In[11]:= marketsolns = Solve @ marketcondition, p D Out[11]= 88 p 45.7143 << In[12]:= marketprice = p ± . marketsolns @@ 1 DD Out[12]= 45.7143 In[13]:= marketquantity = demand @ marketprice D Out[13]= 2214.29 In[14]:= supply @ marketprice D Out[14]= 2214.29 In[15]:= ParametricPlot @88 demand @ p D , p < , 8 supply @ p D , p << , 8 p, 30, 60 < , AspectRatio 1 ± GoldenRatio, AxesLabel 8 "quantity", "price" < , Epilog 8 Text @ "demand", 8 demand @ 50 D , 50 < , 8 1, 1 <D , Text @ "supply", 8 supply @ 35 D , 35 < , 8 1, - 1 <D , Point @8 marketquantity, marketprice <D<D Out[15]= 1800 2000 2200 2400 2600 2800 3000 quantity 35 40 45 50 55 60 price demand supply ± 1. Continuing with the example above, if the population of potential consumers increases by 10%, what will the new price and quantity be? ± Modified program 1
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MMEsupplydemandsoln - 2011 - Steven Tschantz Supply and...

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