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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

 

 

 

 

 

 

 

10

 

Elasticity

MC

 

(P - MC)/P

-1/EP

 

11

 

 

 

 

 

 

 

12

 

-39.0

210

 

0.7308

0.0256

 

13

 

 

 

 

 

 

 

Microeconomics, Economics

  • Category:- Microeconomics
  • Reference No.:- M91549565
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