Question

The U.S. Department of Agriculture is interested in analyzing the domestic market for soybean. The USDA’s staff economists estimate the following equations for the demand and supply curves: The demand curve of soybean is P = 700 - 2Qd, and the supply curve of soybean is: P = 200 + 3Qs where P represents price of soybean in dollars per bushel and Q represents quantity of soybean in bushels.

1. Suppose that the government passes a farm support bill that sets $600 per bushel as the minimum allowable soybean price in the market. How would this minimum price alter this market? Would there be any excess supply of soybean? If so, how much?

Answer 1

Equilibrium is reached when quantity demanded equals the quantity supplied at a particular price. That is at a particular price where quantity demanded equals the quantity supplied is Equilibrium

P = 700 - 2Qd or 2Qd = 700 - P or Qd = 350 - 0.5P

P = 200 + 3Qs or 3Qs = P - 200 or Qs = 1/3P - 200/3

So 700 - 2Q = 200 + 3Q

3Q + 2Q = 700 - 200

5Q = 500

Q = 500/5 = 100 bushels of soyabean (Equilibrium Quantity)

P = 200 + 3* 100 = $500 (Equilibrium Price)

If the minimum price set is $600,

Then

P = 700 - 2Qd or 2Qd = 700 - P or Qd = 350 - 0.5P = 350-0.5*600 = 50

P = 200 + 3Qs or 3Qs = P - 200 or Qs = 1/3P - 200/3 = 1*600/3-200/3 = 200 - 200/3 = 400/3 = 133.3

Surplus/Excess supply = 133.33 - 50 = 83.33