Copyright term:

Recently the Supreme Court upheld Congress's right to extend the term of basic copyright protection to 95 years. There has been a great deal of debate about whether this serves the public welfare. This exercise suggests a (highly simplified) model of the issue.

Suppose that the yearly rate of demand for a creative work is constant and follows the linear curve shown in figure 7.14. The area in the triangular region is A. The marginal cost of production is zero. It follows that the yearly rate of producer surplus, if the product is actually produced, is π = A/2, and if the producer values future surpluses by discounting at the rate r, the total surplus to time T is

The originator will produce the item only if the producer surplus exceeds the fixed cost F of creation. Assume that over the vast assortment of information products with the demand rate of the figure, the cost F is uniformly distributed between 0 and some maximum M. Hence the probability that a given work will be created and marketed is proportional to the total available producer surplus π. Likewise, the expected value F of the fixed cost given that this cost is less than π is π/2. Argue that the expected net benefit to society is proportional to

(a) Assuming that society uses the same discount rate r, give an explicit expression for B (to within a constant multiple).

(b) Show that there is no finite time that maximizes the social objective.

(c) Suppose that the actual demand curve slopes outward at the lower end as indicated by the dashed curve so that the total area under the curve is ρA where ρ > 1. Find the optimal value of T.

(d) Find T when ρ = 1.2 and r = .05.

(e) What is the limit of T as ρ → ∞ in terms of r? Compare with the original 14-year term set by Congress in 1790.