A well-known simple model, applicable for analysing boom-bust cycles in agriculture, but extendable to analysing boom-bust cycles in many different areas of economics is the hog cycle model. As the name suggests, the origin of the model discussed here was in analysing the demand and supply for hogs.
The model consists of the following equations: where B is a demand shifter (e.g. the price of bacon and other pork products) and F is a supply shifter (e.g. the price of food for the hogs).
Q^{d}_{t} = B - P_{t}
Q^{s}_{t} = -F +0.5P_{t-1}
a) Find the price P_{t }that solves above model.
b) Find the homogenous, particular and then general solution for this difference equation i.e. for P_{t}.
c) Setting t = 0 find the solution to the Hog-Cycle model.
d) Analyze the dynamic path of pork prices by finding first the steady state value of prices, and then by assigning initial values to P_{0} =5 and (F + B) = 15 study the evolution of prices.