APPENDIX

311

If a tax be imposed on the monopoly profit, either as
a specific tax, or a percentage of that profit, the curve #QN
is lowered, but the position of its highest point is not moved
to right or to left. Thus, such a tax does not stimulate any
change in supply or price.
Taxes which modify the shape of the cost curve OpzP, may
so modify the shape of the monopoly-profit curve zQN as
to move the point Q either to the right or to the left, thus
changing the scale of supply, and consequently causing a
change in price. If Q were made to move to the left, the
supply would be decreased and the price per unit increased.
If, on the other hand, QQ moved to the right, the supply
would be increased, and the price per unit would be reduced.
We do not propose to examine here the conditions which
might give rise to either of such varieties of change. The
student may find a useful exercise in tracing out the consequences
 of taxes proportional to cost, to output, or varied in
other definite ways.
If the problem of monopoly be treated algebraically, we
have as data that f(z) is the demand price per unit, and
(x) the cost per unit, of a quantity z. The monopoly profit
is therefore z{f(#)—¢(#)}, and if this is to be made
a maximum, the value of 2 must be that found from the
equation
Ax) — ox) + 2{ Ux) — p(x) } =0.

This expresses the condition that the tangents at # and Zin
Fig. (x) are parallel. This is another way of stating that Q
is the highest point of the curve zQN.
In dealing with the problem of rent, we may employ
diagrams of the type of those of Figs. (i) and (ii), constructed
so that the additions to product, resulting from successive
additions to expenditure in cultivation, are represented by
the ordinates of a curve whose absciss® represent the expenditures
 in question, just as, in those figures, the ordinates
represent the utilities of successive additions to a supply, the
amount of which is represented by the corresponding
abscisse. Such diagrams are very useful, and are given in
many text-books. A second mode of representation, corresponding
 rather to the diagrams of Figs. (vi) and (vii), offers
some features of advantage, and students who have familiarised
 themselves with one mode of representation should find
little difficulty, and some gain, in making comparisons
between the two.