469-CH2-MATH

# 469-CH2-MATH - \$95.75 II TO MAXIMIZE PROFITS SET MR = MC SOLVE FOR Q MR = MC 170 40Q = 38 40Q = 132 Q = 3.3 Solve for P P = 170 20(3.3 = \$104 Solve

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SUMMARY OF THE MICROCHIP EXAMPLE Given the Demand Equation , Q = f (P): Q = 8.5 - .05P Calculate the Inverse Demand Equation: .05 P = 8.5 - Q 20 (.05 P) = (8.5 - Q ) 20 P = 170 - 20 Q Solve for, TR, MR and MC TR = P x Q TR = (170 - 20Q) Q TR = 170 Q - 20 Q 2 TC = 100 + 38Q [ FC = \$100 and VC = \$38] MR = 170 - 40Q MC = \$38 I. TO MAX SLS (TR): SET MR = 0, SOLVE FOR Q 0 = 170 - 40Q 40Q = 170 and Q = 4.25 P = 170 - 20 (4.25) = P = \$85 TR = P x Q = 4.25 x \$85 = \$361.25 TC = 100 + 38 (4.25) = \$261.50 Π = TR - TC =

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Unformatted text preview: \$95.75 II. TO MAXIMIZE PROFITS, SET MR = MC, SOLVE FOR Q* MR = MC 170 - 40Q = 38 40Q = 132 Q* = 3.3 Solve for P*: P = 170 - 20 (3.3) = \$104 Solve for TR: TR = P x Q = \$104 x 3.3 = \$343.20 Solve for TC: TC = 100 + 38 (3.3) = \$225.40 Solve for Π Π = \$343.2 - 225.4 = \$117.80 III. TO MAXIMIZE PROFITS: SET MP = 0, SOLVE FOR Q* Π = TR - TC Π = (170 Q - 20 Q 2 ) - ( 100 + 38Q) Π = 170 Q - 20 Q 2- 100 - 38Q Π = -100 + 132 Q - 20 Q 2 MP = 132 - 40Q 0 = 132 - 40Q 40Q = 132 Q* = 3.3...
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## This note was uploaded on 01/23/2012 for the course ECON 469 taught by Professor Staff during the Fall '11 term at University of Michigan.

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469-CH2-MATH - \$95.75 II TO MAXIMIZE PROFITS SET MR = MC SOLVE FOR Q MR = MC 170 40Q = 38 40Q = 132 Q = 3.3 Solve for P P = 170 20(3.3 = \$104 Solve

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