Question

The government has implemented a new policy to support the price of barley at $5.68/bu. If the barley market equilibrium price is $3.52/bu, the equilibrium quantity of barley is 1,117.00 million bu, the elasticity of supply is 0.3, and the elasticity of demand is -0.75, then what is the new quantity supplied and the new quantity demanded at the support price? How much barley would the government need to buy to keep the price supported at $5.68/bu?

Answer 1

The % change in price from the equilibrium price = (5.68 - 3.52)/3.52 * 100 = 2.36/3.52 * 100 = 0.67 * 100 = 67%

The elasticity of demand is -0.75 i.e. % change in demand/ % change in price = -0.75.

or, % change in demand/67 = -0.75

% change in demand = 67 * (-0.75) = - 50.25%

So, demand will go down by 50.25%. So, new demand will be = 1,117.00 million bu - 50.25% of 1,117.00 = 1,117 - 561.29 = 555.71 million bu.

The elasticity of supply is 0.3 i.e. % change in supply/ % change in price = 0.30

or, % change in supply/67 = 0.30

% change in supply = 67 * (0.30) = 20.10%

So, supply will go up by 20.10%. So, new supply will be = 1,117.00 million bu + 20.10% of 1,117.00 = 1,117 + 224.52 = 1341.52 million bu.

The new quantity supplied at the support price is = 1341.52 million bu and the new quantity demanded at the support price = 555.71 million bu.

So, there will be a surplus of (1341.52 - 555.71) million bu = 785.81 million bu. So, the government will have to buy this surplus 785.81 million bu to keep the price supported at $5.68/bu.