The market for wheat is described by the linear demand curve $Q_d = 4800 - 8P$ and the linear supply curve $Q_s = -800 + 6P$, where $P$ is the price in dollars per tonne and $Q$ is quantity in thousands of tonnes.

(a) Find the competitive equilibrium price and quantity.

(b) The government introduces a price floor of \$500 per tonne. Compute the quantity demanded, quantity supplied, the surplus (excess supply), and the total cost to the government of purchasing the surplus at the floor price.

(c) Calculate the dead‑weight loss associated with the price floor.

(d) The government also pays a subsidy to producers equal to half the surplus per unit (i.e., $\frac{1}{2}$ of the difference between the floor price and the equilibrium price). Determine the total subsidy payment and the overall government outlay (purchase cost plus subsidy).

Question

The market for wheat is described by the linear demand curve $Q_d = 4800 - 8P$ and the linear supply curve $Q_s = -800 + 6P$, where $P$ is the price in dollars per tonne and $Q$ is quantity in thousands of tonnes.

(a) Find the competitive equilibrium price and quantity.

(b) The government introduces a price floor of \$500 per tonne. Compute the quantity demanded, quantity supplied, the surplus (excess supply), and the total cost to the government of purchasing the surplus at the floor price.

(c) Calculate the dead‑weight loss associated with the price floor.

(d) The government also pays a subsidy to producers equal to half the surplus per unit (i.e., $\frac{1}{2}$ of the difference between the floor price and the equilibrium price). Determine the total subsidy payment and the overall government outlay (purchase cost plus subsidy).

Accepted Answer

Equilibrium: $400, 1,600 k t. Floor price: demand 800 k t, supply 2,200 k t, surplus 1,400 k t, purchase cost $700 m. DWL $70 m. Subsidy $50/t, total subsidy $70 m. Total outlay $770 m.

Gce Model Questions Vol1 2018 Economics Question 10

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