The national accounts treat all government purchases of goods and services, G, as part of real GDP. But suppose that the public services derived from government purchases are an input to private production, say: Y = F(κK, L, G)
In this case, public services are an intermediate product-a good that enters into a later stage of production. Hence, we ought not to include these services twice in real GDP-once when the government buys them and again when the services contribute to private production.
a. Suppose that businesses initially hire private guards. Subsequently, the government provides free police protection, which substitutes for the private guards. Assume that the private guards and public police are equally efficient and receive the same wage rates. How does the switch from private to public protection affect measured real GDP?
b. How would you change the national accounts to get a more accurate treatment of government purchases of goods and services? Is your proposal practical?