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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.
A
B
C
D
E
F
G
1
2
THE OPTIMAL PRICE FOR SPARE PARTS
3
4
5
Price
Quantity
Revenue
Cost
Profit
6
7
780
10
7,800
22,050
-14,250
8
9
Elasticity
MC
(P - MC)/P
-1/EP
11
12
-39.0
210
0.7308
0.0256
13
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