An ambient differentiated emission permit gives the holder the right to emit anywhere provided emissions have no more impact on receptor \(j\) than one unit of emissions at source \(i\). Let \(l_{i}^{l}\) be the quantity of such permits a firm holds.

a. Suppose there is only one receptor and \(\mathrm{K}\) sources. Write an equation showing allowed emissions for source \(k\) if it holds a portfolio of ambient differentiated emission permits \(\left\{l_{1}, l_{2}^{1}, \ldots, l_{\mathrm{k}}\right\}\).

b. Generalize your answer to part (a) for the case of multiple receptors.