Graphing functions: An example with a demand function.Oct 2, 2013Assume, for example, the following demand function for ski days at theSteamboat ski area.Dssb= 20 + :03(snowsb) :06psb+ :01pv ailwhere Dssbis the individual’s demand, this year, for Steamboat ski days.snowsbis Steamboat’s total snow fall, last year, in inchespsbis the cost of a steamboat ski day, measured in dollarspv ailis the cost of a vail ski day day, measured in dollars.How many days will the individual ski if it cost nothing to ski at SB or Vailand last year SB got 500 inches of snow?How many fewer days will the individual ski SB if the cost of skiing SBincreases by $50/day?1Graph the demand function with Dssbon the vertical axis and psbon thehorizontal axis, assuming snowsb= 300 and pv ail= 100.In this case the demand function isDssb= 20 + :03(300) :06psb+ :01(100) = 30:0 0:06psb0 100 200 300 400 5000102030psbDssbDsbbas a function psbassum. snowsb= 300 and pv ail= 100Could I have graphed this function if I had not spe…cied snowsband pv ail?No.Figure out exactly how this graph is a¤ected if snowsb400 inches ratherthand 300 inches. If pv ailis $120 rather than $100.2Now graph the demand function with Dssbon the vertical axis and snowsbon the horizontal axis, assuming psb= 80 and pv ail= 100Dssb= 20 + :03(snowsb) :06(80) + :01(100) = 16:2 + 0:03snowbs0 100 200 300 400 500 600 700 800 900 1000202530354045snowsbDssbDsbbas a function of snowsbassum. psb= 80 and pv ail= 100What do es this demand function (demand as a function of snowfall) tell us?What would this curve do if psbincreased from $80 to $120?3Now graph the …rst restricted demand function, Dssb= 30:0 0:06psb, butwith $ on the vertical axis and ski days on the horiziontal axis.(‡ip the paper)if Dssb= 30:0 0:06psbthen solving for psbpsb= 500:0 16: 667Dssb– price as a function of quantity rather thanquantity as a function of price.Written this way, the demand function is often called the "inverse demandfunction" or the mwtp (marginal wtp function). We typically simply call themdemand functions.The individual would pay for $500 for the his …rst S B ski but $500 $16:667for his second ski day and $500 $16:667 $16:667 for his third SB ski day.Graphing the inverse demand function0 2 4 6 8 10 12 14 16250300350400450500Dssbmwtpmtwp for additional SB ski day as a function of SB ski days.How would this curve shift is snowsbdecreased from 300 to 100?When you are through with these notes you should be able to graph Dssborpsbas function of any of the other variables, and b e able to …gure out how thatgraph would shift is something not graphed changes
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