With a 25 per case unit sales tax the tax ridden sup

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, with a $25 per case unit sales tax, the “tax-ridden” sup- ply curve is P S + T = P S + 25 = 45 + 0.1 Q S . In contrast, with a 25 % ad valorem sales tax, the tax-ridden supply curve is P S (1 + t ) = P S (1.25) = 25 + 0.125 Q S . Setting the two expressions equal, we calculate that Q S = 20/ 0.025 = 800 units, at which point the price facing buyers with either tax is $125/case. (b) With the 25% ad valorem sales tax, we get the equation P S (1 + t ) = P S (1.25) = 25 + 0.125 Q S . When Q S = 150 cases, the price facing buyers = 25 + 0.125(150) = $43.75/case. Without any tax, the price would have been P S = 20 + 0.1(150) = $35/case. The unit tax must therefore be 43.75 – 35 = $8.75/case. 7. (a) For Sal, y = 2 x , while for Slim, y = (1/3) x , as shown in the diagram below. For Sal, with y = 120 – (2/3) x = 2 x , x = (3/8)(120) = 45 loaves of Bread and y = 2 x = 2(45) = 90 containers of Jam. Using the same method, Slim will initially consume 120 loaves of Bread and 40 containers of Jam. (b) With the increase in the price of Bread, the effect of which is to lower the real income of both Sal and Slim, Sal consumes 36 loaves of Bread and 72 containers of Jam , while Slim consumes 72 loaves of Bread and 24 containers of Jam. Note that Sal’s consumption of both goods has dropped by (72 – 90)/90 = (36 – 45)/45 = –0.2 = 20%, but that Slim’s consumption of both goods has dropped by (24 – 40)/40 = (72 – 120)/120 = –0.4 = 40%! The reason is that before and after the Bread price increase, Slim was spending a higher proportion of his income on Bread, and so the effect of the price increase on his real income was greater than it was on Sal’s. [For both Sal and Slim, Bread and Jam are perfect complements in consumption. Perfect complements in consumption are discussed in Chapter 3 and Appendix 3 of the text, while perfect complements in production are discussed in Chapter 9 and Appendix 9 of the text.] M3-2 MATH MODULE 3: SOLUTIONS TO EXERCISES
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8. Using substitution, we have for Duopolist 1: Q 1 = R 1 ( Q 2 ) = 35 – 0.5 Q 2 = 35 – 0.5(40 – 0.5 Q 1 ) = 15/ 0.75 = 20 units, and hence for Duopolist 2, Q 2 = 30 units and total indus- try output Q = 20 + 30 = 50 units.
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