Question

Exercise 14.8

The Pear Computer Company just developed a totally revolutionary new personal computer. Pear estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be

P=2,500−500QP=2,500−500Q

where QQ is millions of computers. The marginal (and average variable) cost of producing the computer is $900.

Assuming Pear acts as a monopolist in its market, the profit-maximizing price and output levels are

per computer and

million computers, respectively. The total contribution to profits and fixed costs at this output level is

million.

Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years:

Complete the following table by calculating the contribution to profit and overhead for each of the 10 time periods and prices.

Time Period	Price	Quantity Sold	Total Contribution
	($)	(Million)	($ Million)
1	2,400	0.2
2	2,200	0.2
3	2,000	0.2
4	1,800	0.2
5	1,700	0.2
6	1,600	0.2
7	1,500	0.2
8	1,400	0.2
9	1,300	0.2
10	1,200	0.2

Over the 10 periods, the total contribution to profits and fixed costs from price skimming is

million.

Answer 1

Given the demand function is P=2,500-5000. The marginal and average variable cost of producing the computer is $900. Calculate Total Revenue: TR=PxQ = (2,500 – 5009) = 2,5000-5000? Calculate Marginal Revenue: MR = STR dQ = (2,500Q – 5009) = 2500 – 10000 do

Profit maximizing point is where MR = MC MR = MC 2500 – 1000Q =900 1000Q =1,600 Q=1.6 Substitute Q in P: P=2,500-5009 = 2,500-500(1.6) = 2,500-800 = $1,700 Calculate Profit: T=TR-TC =(PxQ)-(AVCxQ) =(1,700x1.6)-(900x1.6) = 2,720-1, 440 = $1,280 The Profit maximizing price is $1,700, quantity is 1.6 Units, fixed cost does not exist and the profit is $1,280

Below is the complete table: 2 A AVC 480 TC 900 900 9001 2200 4401 260 WN 0.21 Quantity Time Sold 1 Period Price ($) (Millions) TR 1 2400 0.2 0.2 2000 1800 15 1700 0.2 1600 0.2 7 1500 14001 1300 11 10 1200 0.2 00 VOUWN- 0.2 900) Total Contribution ($ million) 1801 300 180 180 220 180 180 180 180 140 180 120 1801 100 180 180/ 601 160 400 360 340 320 3001 280 260 240 1600 au 0.21 0.21 0.21 900 900 900 900 900 9001

Below table shows the formulas used for the calculation: A B C Time 1 Period 2 1 3 2 10.2 Quantity Sold Price ($) (Millions) 2400 0.2 2200 0.2 2000 1800 1700 1600 1500 1400 0.2 4 5 900 3 4 0.2 O Total Contribution ($ million) =(D2-F2) =(D3-F3) =(D4-F4) =(D5-F5) =(D6-F6) =(D7-F7) =(D8-F8) =(D9-F9) 1=(D10-F10) =(D11-F11) 10.2 TR AVC =(B2*C2) 900 =(B3*C3) 900 =(B4*C4) =(B5*C5) 900 =(B6*C6) 900 =(87*C7) 900 =(B8*C8) 900 =(B9*09) 900 =(B10*010) 900 =(B11*c11) 900 TC =(E2*C2) 1=(E3*C3) =(E4*C4) =(E5*C5) =(E6*C6) =(E7*C7) =(E8*C8) 1=(E9*09) 1=(E10*С10) =(E11*c11) 6 5 7 6 8 7 9 8 10 9 11 10 0.2 1300 0.2 1200 10.2