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Show As shown in Figure F- 3, an ad valorem tax can be represented by a downward rotation of the demand curve. If the industry is one of constant costs over the relevant range ( d = o) it can be shown that the change in price is as follows: Ap = cr 1 - r and thus varies directly with the intercept of the supply function. It is useful to note that in general the price increase is dependent upon both the intercepts and the slopes of the supply and demand equations. Units 1 - P Units Figure F- 3. Competitive Industry. Qfl being produced and sold at a price P0. A unit tax of BD is now levied. The new demand curve becomes CD with marginal revenue curve DH. The new equilibrium is at R with Qj units produced and sold at a price The ad valorem tax under monopoly is illustrated in Figure F- 4. With linear cost and demand curves and an ad valorem tax rate r, and with constant cost ( d = p) the price change will be: Figure F- 2. Monopoly. AP = 1/ 2 [ fh] MONOPOLY In the case of the monopoly, if we begin with the demand function p = a + bx and the cost function C = c + dx, and a unit tax of t is introduced, the change in price is as follows: Ap = 2( b- d) t which is one- half the change under the competitive case ( this is always true with linear functions since the marginal revenue curve has twice the slope of the average revenue curve). Again for the case of constant cost ( d= 0) we find that Ap= V2t. In Figure F- 2 the monopoly case is shown with initial demand curve AB, marginal revenue curve BK and cost curve of EF. Initial equilibrium is at N with It will be noted that this again represents exactly half the price change noted under the unit tax. Figure F- 4 is labeled as the other diagrams and its analysis is similar. B P 1 - -\ r--\ pd D '" \ 1 i \ > F Gi E^ ^ R\ far- J \ ISA \ 0 Q, Qn K 1 0 Figure F- k. Monopoly. A 90 |