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 $\mathbf{1}\mathbf{,}\mathbf{600}\mathbf{-}\mathbf{2}{\mathbf{P}}_{\mathbf{desktop}\mathbf{}}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{6}\mathbf{M}$(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 systems’ primary consumer demographic would increase 4.2 percent this year to$\mathbf{\backslash (}\mathbf{61300}$and that the selling price of a desktop would decrease to$\mathbf{\backslash )}\mathbf{980}$, both of which the CEO viewed favorably for Viking. In a related article, the CEO read that the upcoming year’s projected demand for $\mathbf{11}\mathbf{,}\mathbf{200}\mathbf{-}\mathbf{100}{\mathbf{P}}_{\mathbf{memory}\mathbf{}}\mathbf{-}\mathbf{2}{\mathbf{P}}_{\mathbf{desktop}\mathbf{}}$desktop memory modules is Qd memory 2Pdesktop (in thousands of units), where Pmemory is the market price for a$\mathbf{512}\mathbf{MB}$memory module and Pdesktop 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 tofirms. Furthermore, suppose that Viking’s CEO commissioned an industrywide study to examine the industry capacity for$\mathbf{512}\mathbf{MB}$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$\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{2}{\mathbf{P}}_{\mathbf{memory}\mathbf{}}\mathbf{+}\mathbf{N}$(in thousands), where Pmemory is the price of a$\mathbf{512}\mathbf{MB}$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$\mathbf{512}\mathbf{MB}$modules supply an equal share to the market. How would your report change if the price of desktops were$\mathbf{\$}\mathbf{1080}$? What does this indicate about the relationship between memory modules and desktop systems?

Short answer

The anticipated desktop systems will be$36,240$ units. The price of a desktop memory module is $$65.12$ and a total of $2.728$million quantity of memory modules will be supplied by the market as a whole.

Each firm should produce as 3 units. The new price of memory modules is $$63.52$ and a total of $2.688$million quantity of memory modules to be separated and each firm should produce as a 27 units.

Step-by-step solution

Information given

Given the values are

$\begin{array}{c}{\mathrm{P}}_{\mathrm{desktop}}=980\\ \mathrm{M}=\mathrm{\$}61,300\end{array}$

Finding the anticipated desktop systems:

To determine the anticipated desktop systems, we need the following calculations -

$\begin{array}{c}{\mathrm{Q}}_{\mathrm{desktop}}^{\mathrm{d}}=1,600-2{\mathrm{P}}_{\mathrm{desktop}}+0.6\mathrm{M}\\ {\mathrm{Q}}_{\mathrm{desktop}}^{\mathrm{d}}=1,600-2{\mathrm{P}}_{\mathrm{desktop}}+0.6\mathrm{M}\\ =1,600-(2\times 980)+(0.6\times 61,300)\\ =1,600-1,960+36,780\\ =36,420\end{array}$

Thus, the anticipated desktop systems will be $36,420$ units.

The demand function of $100$suppliers will be

${\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{d}}=11,200-100{\mathrm{P}}_{\mathrm{memory}}-2{\mathrm{P}}_{\mathrm{desktop}}$

This market also supplies the memory module according to the supply function

${\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{s}}=1,000-2{\mathrm{P}}_{\mathrm{memory}}+\mathrm{N}$

With 100 suppliers, the memory module the function will be

${\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{s}}=1,000+25{\mathrm{P}}_{\mathrm{memory}}$

Finding the equilibrium in markets:

To determine the equilibrium in both markets, balance the demand and supply of memory modules are

$\begin{array}{c}{\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{d}}={\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{s}}\\ 11,200-100{\mathrm{P}}_{\mathrm{memory}}-2{\mathrm{P}}_{\mathrm{desktop}}=1,000+25{\mathrm{P}}_{\mathrm{memory}}+100\\ 10,100-125{\mathrm{P}}_{\mathrm{memory}}-2\times 980=0\\ {\mathrm{P}}_{\mathrm{memory}}=65.12\end{array}$

Using the price, we get supply as -

${\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{s}}=2.728$

Thus, the price of a desktop memory module is $65.12$and a total of $2.728$million quantity of memory modules you be supplied by the market as a whole. Each firm should produce as 3 units.

Finding the new equilibrium in markets

To calculate the new equilibrium price and quantity with price $1080, we need the following calculations –

$\begin{array}{c}{\mathrm{Q}}_{\mathrm{desktop}}^{\mathrm{d}}={\mathrm{Q}}_{\mathrm{desktop}}^{\mathrm{S}}\\ 11,200-100{\mathrm{P}}_{\mathrm{memory}}-2{\mathrm{P}}_{\mathrm{desktop}}=1,000+25{\mathrm{P}}_{\mathrm{memory}}+100\\ 10,100-125{\mathrm{P}}_{\mathrm{memory}}-2\times 1,080=0\\ {\mathrm{P}}_{\mathrm{memory}}=63.52\end{array}$

${\mathrm{Q}}_{\mathrm{memory}}^{\mathrm{s}}=2.688$

The new price of a memory modules are $$63.52$and a total of $2.688$million quantity of memory modules to be separated and each firm should be produce as a 27 units.

Thus, we can conclude that the relationship between memory modules and desktop systems is positive. When the price of memory modules increases, the price of desktop systems also moves in the same direction. The same rule applies to demand and supply also.