Answer to Question #237507 in Economics for Sniper

Question

The supply of many agricultural products is based on the price of the product in the previous
year. If prices were high in year 1 more of the product will be planted in year 2 in the
expectation that prices will remain high. This may cause an oversupply, resulting in lower
prices.
Because of the low prices in year 2, less of the product will be planted in year 3, resulting in
higher prices. (This is based on the adaptive expectations hypothesis, where expectations are
based on past behaviour).
Due to the delay in production time, supply and demand do not interact to reach equilibrium in
the short term, and this process may continue for a number of years.
Given a demand curve Qdt = 150 -3Pt and a supply curve Qst = -50 + 2Pt-1, and given P0 = 48
at time t = 0,
a) Find the equilibrium price and quantity.
b) Plot the price for the first 10 years.

Answer 1

a) The equilibrium price and quantity are:

Qdt = Qst,

150 - 3Pt = -50 + 2Pt-1,

2Pt-1 + 3Pt = 200,

If t = 1, then Pt-1 = 48,

2×48 + 3Pt = 200,

3Pt = 104,

Pt = 34.67.

Qt = -50 + 2×48 = 46 units.

b) The price for the first 10 years will periodically increase and decrease.