Question

"The market demand for coffee is described by the equation Q_D = 20 - 2P, and the market supply is given by Q_S = 2 + P, where P is the price in $ per pound, and the quantities are measured in million pounds per year.

(a) Calculate the price, quantity, consumer surplus, and producer surplus in the free-market equilibrium.

(b) Demonstrate that the price consumers pay for coffee remains the same under three policies: an excise tax of $6 per pound, a production quota of 4 million pounds per year, and a price floor of $12 per pound. How does consumer surplus differ in each of these three cases?

(c) In which form of intervention will we anticipate the producers in the market to be the efficient suppliers, meaning those with the lower production cost?

(d) Which of these three policies will the producers prefer? (Hint: compare the producer surplus under the three policies.)

(e) Which of these three policies results in the lowest deadweight loss?"

Answer 1

The free-market equilibrium price for coffee is calculated at $6 per pound with a quantity of 8 million pounds per year. The consumer and producer surplus would vary under different market policies. The lowest deadweight loss occurs with the policy that least distorts the market, and producers prefer the policy that maximizes their surplus.

Step-by-step explanation:

To calculate the free-market equilibrium for the coffee market, we set the supply and demand equations equal to each other. This equates
`Q_D = Q_S`, giving us
`20 - 2P = 2 + P`. Solving for P, the equilibrium price, we find that P = 6. Therefore, at the equilibrium price of $6 per pound, the equilibrium quantity (Q) can be calculated by substituting P into either the demand or supply equation:
`Q = 20 - 2(6) = 8` million pounds per year. Consumer surplus can be visualized as the area under the demand curve and above the equilibrium price. The producer surplus is the area above the supply curve and below the equilibrium price. To calculate these surpluses, we would typically use the areas of triangles and/or rectangles formed by these curves and a horizontal line at the equilibrium price. The effects of the three policies (excise tax, production quota, and price floor) on consumer surplus will vary due to the changes in market dynamics each policy would introduce. Under each policy, the lowest deadweight loss would be associated with the policy that least distorts the market from the original equilibrium. Producers will likely prefer the policy that results in the greatest producer surplus, which will depend on how each policy affects the market structure and their costs. In terms of efficiency and least distortion, producers are expected to be efficient suppliers in a scenario that is closest to the free-market outcome, which presumes minimal government intervention.