The only difference is that we assume that 0 whereas

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The only difference is that we assume that, ≥ 0, whereas the demand elasticity is assumed ≤ 0. If = 0, then P = 1, and Q = K (the case of the perfectly inelastic supply curve). If > 0, however, then a constant-elasticity supply function must begin at the origin, since when P = 0, P = 0, and hence Q = 0. In Figure M.8.1, three constant-elas- ticity supply functions are shown. If = 1, then Q = KP 1 = KP, which is a straight line through the origin with slope ∆ P/ Q = P/Q = K. Any supply curve that is a ray or straight line from the origin has unitary elasticity of supply. If > 1, we say that it is elastic, and if < 1, we say that it is inelastic. MATH MODULE 8: SOME SPECIAL FUNCTIONS AND FORMULAS M8-3 P O Q ε S > 1 ε S = 1 ε S < 1 FIGURE M.8-1

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2. Exercises 1. Evaluate the following, using mainly brainpower for (a) to (k) and calculator power for (l) and (m): (a) 6 7 / 6 9 ; (b) 6 9 / 6 7 ; (c) 3 a 4 / 6 a 3 ; (d) 12 3 – 5 ; (e) (3 a ) 2 (3 a ) 3 ; (f) 3 a 2 (3 a ) 3 ; (g) 16 1.5 / 4 2 ; (h) 4 132 / 2 265 ; (i) (1/4) –0.5 ; (j) 2 4 / 4 2 ; (k) ( 2) 6 ; (l) ( 2) 1.5 [to 3 decimal places]; (m) 17 2/5 . 2. (a) For cases (i) to (iv), calculate the logarithms to base 10 and to base e : (i) 10; (ii) e ; (iii) 100; (iv) e 2 . (b) For each case, calculate the ratios log/ ln and ln /log. (c) Calculate the ratios (iii)/(i) and (iv)/(ii) for both log and ln results. TR measured in \$/period. The Total Cost (TC) function is initially TC = 0.5 Q , with Total Costs also measured in \$/period. Profits (in \$/period) = TR – TC. M8-4 MATH MODULE 8: SOME SPECIAL FUNCTIONS AND FORMULAS
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• Fall '12
• Danvo
• Supply And Demand, Natural logarithm, Special functions, Math Module

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