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Answers to Second Test in ECMA04H Version of test with date written as “November 11, 2005” 1. Demand is given by P = 60 - .05X. Supply is horizontal at P = 20. Initial equilibrium is at P = 20, Q = 800. Government levies \$4 tax so that S + T is given by P = 24. Therefore, 60 - .05X = 24, or X = 36/.05 = 720. Tax revenue is therefore 4 x 720, or \$2,880. The correct answer is (N). 2. Excess Burden of a tax is given by [(800 – 720) x 4]/2 = \$160. The correct answer is (P). 3. If a flat-rate tax of “T” is levied in this industry, we will have 60 - .05X = 20 + T or X = (40 – T)/.05 = 800 – 20T. The tax revenue will then be TX (the per unit amount of the tax times the quantity “X” of tesseracts sold. Tax Revenue = T(800 – 20T) = 800T – 20T 2 . To find the tax rate which yields the most tax revenue, we take the derivative of this expression for tax revenue, and set it equal to zero. So, dTR/dT = 800 – 40T = 0 or T* = 20. The correct answer is (L). 4. You should draw most of these alternatives on a graph to determine correct answers. The excess burden of a tax is larger if the demand is more elastic (because more consumers change their consumption patterns and stop consuming the good). For the same reason, however, the revenue raised by a tax will be smaller if the demand is more elastic. If the demand for a commodity is completely inelastic, no consumers stop consuming the good when it is taxed; therefore the excess burden of the tax will be zero. If the demand for a commodity is perfectly elastic, it is true that the sellers will bear the entire burden of the tax, but it is still possible to raise tax revenue so the final statement is untrue. Therefore, Statements I and III are correct. The correct answer is (F). 5. The production function is q = (10KL)/(K+L). In the short run, K = 10. Therefore, the short run production function is q = 100L/(10+L). The marginal product of labour in the short run can be found by using the quotient rule as dq/dL = [100(10+L) – 1(100L)]/(100 + 20L + L 2 ).

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Therefore, dq/dL = [1000 + 100L – 100L}/(100 + 20L + L 2 ). When L = 15, dq/dL = 1000/(100 + 300 + 225) = 1.6. The correct answer is (F). 6. The price of labour is \$12 per unit and the number of units of labour
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