1. Imagine that there is a representative importer whose profits (in the absence of fees for biosecurity clearance at customs) are R(Q), where Q is quantity imported. There is also a representative farmer, whose output is q and profits (in the absence of fees or an incursion of an animal or plant disease) are r(q). However, if an incursion would affect the farmer with probability π, and cause her damage amounting to a proportion θ of her profits, then her expected profits (still in the absence of fees) would be r(q)(1-πθ).
In order to screen Q units of imports and keep the risk of an incursion down to π, border control must incur costs of c(Q;π)
a) First consider the socially efficient choices of Q, q and π. Take first-order conditions with respect to each of these variables, when maximising joint expected value. Here, joint expected value is the profit of the importer plus the expected profit of the farmer minus the costs of border control. You donít have to worry about any fees yet as they are just transfers. Interpret the first-order conditions.
So the function I got is R(Q)+r(q)(1-πθ)-c(Q;π), and I'm not sure where to go from here. I guess I'm confused because they're all symbols and no numbers. Help is appreciated!