Consider the following mathematical description of the market for parsnips.

(1) the demand function:

QD = 100 – 3/2P

 (2) the supply function:

QS = 1/2P

 • What is the equilibrium price and quantity for parsnips?

 Let's elaborate the supply equation by making it dynamic.

 It takes a year to grow parsnips (they should be harvested in March).  Equation (2) describes the behavior of the farmer at planting time (March), we must change the Q_S to Q_P and then add equation (3) Q_S,t = Q_P,t-1.  The Q_S (harvest) is equal to last year’s quantity planted Q_P,t-1.

 Let's use a spreadsheet to explore this model.  Set up the spreadsheet shown below.  The years should run down to 1920

•In cell B2 enter the equilibrium quantity you found above 

•In cell C2 enter the market clearing equation, that is the quantity demanded must equal the harvest (“B2”).

• In cell D2 enter the price equation, that is the inverse demand function—equation (1) solved for price.  This is the price that will  cause the quantity demanded to just equal the harvest.

• In cell E2 enter the planting supply equation —equation (2).  Finally, in B3 enter our new equation, the harvest is equal to last year’s planting.

• Finally, fill columns B through E down through the year 1920.

If you have done everything correctly the market should be boringly stable!  Now comes the fun.

In 1904 the pernicious parsnip pest destroys 25% of the crop.  Add a minus 10 to the equation in cell B6.  What happens?  In technical terms we have placed a dynamic system into a stable (stationary state) and then shocked it.  You might want to create some time series graphs of price and quantity.

If things have gone fairly well, you might want to do some further exploration.

• Change the underlying equations to:

(1) the demand function:

QD = 100 - P

(2) the planting supply function:

QP = 1.1P

redo everything above.  When you set up the original (1900) conditions be careful to use the new equilibrium quantities.  Now what happens when you shock the system?

Hand in the graphs or spreadsheets or both with some explanation for each one.