Question

Viking InterWorks is one of many manufacturers that supplies memory products to original equipment manufacturers (OEMs) of desktop systems. The CEO recently read an article in a trade publication that reported the projected demand for desktop systems to be:

Qd_desktop = 1600 - 2P_desktop + 0.6M (in millions of units), where P_desktop is the price of a desktop system and M is consumer income.

The same article reported that the incomes of the desktop system’s primary consumer demographic would increase 4.2 percent this year to $61,300 and that the selling price of a desktop would decrease to $980, both of which the CEO viewed favorably for Viking. In a related article, the CEO read that the upcoming year’s projected demand for 512 MB desktop memory modules is:

Qd_memory = 11,200 - 100P_memory - 2P_desktop (in thousands of units), where P_memory is the market price for a 512 MB memory module and P_desktop is the selling price of a desktop system.

The report also indicated that five new, small start-ups entered the 512 MB memory module market bringing the total number of competitors to 100 firms. Furthermore, suppose that Viking’s CEO commissioned an industry-wide study to examine the industry capacity for 512 MB memory modules. The results indicate that when the industry is operating at maximum efficiency, this competitive industry supplies modules according to the following function:

Qs_memory = 1000 + 25P_memory + N where P_memory is the price of a 512 MB memory module and N is the number of memory module manufacturers in the market.

Viking’s CEO provides you, the production manager, with the above information and requests a report containing the market price for memory modules and the number of units to manufacture in the upcoming year based on the assumption that all firms producing 512 MB modules supply an equal share to the market.

Round to 2 decimals

A) Market Price for Memory Modules ($):

B) Number of units to manufacture (thousand):

How would your report change if the price of desktops were $1,080?

C) Market Price for Memory Modules ($):

D) Number of units to manufacture (thousand)

Please clearly indicate what number goes with what letter!

Answer 1

Below is the projected demand and supply equations of memory modules:

Qd_memory = 11,200 - 100P_memory - 2P_desktop

Qs_memory = 1000 + 25P_memory + N

A) Given the initial projected price of the of desktop = $980 and the number of firms manufacturing memory modules = 100, the market price of memory modules is given by the condition where quantity demand and quantity supplied of the memory modules is equal.

                    Qd_memory   = Qs_memory

11,200 - 100P_memory - 2P_desktop = 1000 + 25P_memory + N

11,200 - 100P_memory – 2(980) = 1000 + 25P_memory + 100

11,200 - 100P_memory - 1960 = 1000 + 25P_memory + 100

9240 - 100P_memory = 1100 + 25P_memory

              9240 – 1100 = 25P_memory + 100P_memory

              8140 = 125 P_memory

              P_memory = 8140/ 125

              P_memory = $65.12

B) Number of units to be manufactured be :

Qs_memory = 1000 + 25P_memory + N

Qs_memory = 1000 + 25(65.12) + 100

Qs_memory = 1000 + 1628 + 100

Qs_memory = 2728 (thousand)

C) If price if desktop changes to P_desktop = $1080, then the market price of memory modules changes to :

11,200 - 100P_memory - 2P_desktop = 1000 + 25P_memory + N

11,200 - 100P_memory – 2(1080) = 1000 + 25P_memory + 100

11,200 - 100P_memory – 2160 = 1100 + 25P_memory

9040 - 100P_memory = 1100 + 25P_memory

9040 – 1100 = 125 P_memory

7940 = 125 P_memory

P_memory = 7940/125

P_memory = $63.52

D) Number of units to be manufactured be :

Qs_memory = 1000 + 25P_memory + N

Qs_memory = 1000 + 25(63.52) + 100

Qs_memory = 1000 + 1588 + 100

Qs_memory = 2688 (Thousand)