Let's revisit the maker of spare parts in Problem S1 of Chapter 2 to determine its optimal price. The firm's demand curve is given by Q = 400 -.5P and its cost function by C = 20,000 + 200Q +.5Q2:
a. Treating price as the relevant decision variable, create a spreadsheet (based on the example shown) to model this setting. Compute the price elasticity in cell B12 according to EP = (dQ /dP)(P/Q ).
b. Find the optimal price by hand. (Hint: Vary price while comparing cells E12 and F12. When (P - MC)/P exactly equals -1/EP, the markup rule is satisfied and the optimal price has been identified.)
c. Use your spreadsheet's optimizer to confirm the optimal price.
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A
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B
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C
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D
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E
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F
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G
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1
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2
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THE OPTIMAL PRICE FOR SPARE PARTS
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3
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4
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5
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Price
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Quantity
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Revenue
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Cost
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Profit
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6
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7
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780
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10
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7,800
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22,050
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-14,250
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8
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9
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10
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Elasticity
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MC
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(P - MC)/P
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-1/EP
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11
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12
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-39.0
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210
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0.7308
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0.0256
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13
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