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  • CG 4:06 pm on January 26, 2014 Permalink | Reply
    Tags: business, computer architecture, economy, price elasticity   

    Amdahl’s Law and Price Elasticity 

    I have just noticed that Amdahl’s Law used in measuring processor performance is similar with the Price Elasticity Law (I read from the book “Starbucks (Corporations that Changed the World) – Marie Bussing-Burks”) in economic concepts.

    The same principle is that there is a limit in increasing processing performance to get more throughput, or to rephrase it in business language: there is a limit in reducing price of an item to get more revenue.

    Amdahl’s Law says that speedup is how a machine performs after enhancement. A SpeedUp(E) = Performance with E / Performance without E = Execution time without E / Execution time with E. Execution time = Execution time unaffected + (Execution time with E / Amount of improvement).

    (Notes: Examples is taken from EL 2244 Course being taught at ITB this semester. The reference book is John L. Hennessy and  David A. Patterson , Computer Organization and Design: The Software Hardware Interface, Morgan Kaufmann Publishers, 4th Edition, 2009.)

    Ex. 1:

    A program runs in a machine in 10s. 50% of the time is doing multiplications. If we improve the multiplication unit so it runs twice as fast, how big is the speed up?

    Answer:

    Exec_time(E) = (Affected_exec_time/improvement) + unaffected_exec_time

    = (5s/2) + 5s = 7,5 s

    Speed_up(E) = 10s/7,5s = 1,333  which is not 2 times faster

    Ex. 2:

    A program runs for 10s. 70% of the time is doing additions. How much improvement on the additions if we want to reduce the running time to 3s?

    Answer:

    Exec_time(E) = (Affected_exec_time/improvement) + unaffected_exec_time

    3s = (7s/n) + (10-7)s

    3s = (7s/n) + 3s

    0 = 7s/n

    No amount of improvement can reduce the running time to 3s.

    Now let’s see the Price Elasticity Law. Price Elasticity (E) = % change in quantity demand / % change in price.

    Ex 1:

    If we reduce the price of 36 inch TV from $450 to $400, the average price would be $425. The absolute value of percentage change = $50/$425 = 0.118. Number of unit sold is increased from 200 to 300 so the average number of unit sold = 250.

    So the percentage  of change in quantity demand is 100/250 x 100% = 40%.

    The price elasticity = 0.4/0.118 = 3.39%

    If the absolute value of price elasticity is between 0 – 0.99, demand is inelastic. Necessity items like coffee, milk, gasoline, prescription drugs are tend to be relatively insensitive to price change.

    Ex 2:

    A store manager drops the price of a gallon of milk from $4 to $3. The average price will be $3.5. The absolute value of % change = $1/$3.5 = 0.29

    Milk sold going from 10 to 11. The average number of gallon sold = 10.5. Percent of change in quantity demand = 1/10.5 = 0.1.

    Price elasticity = 0.1/0.29 = 0.34. The demand is inelastic.

    So if demand is elastic, a price cut will increase total revenue (and an increase in price will mean lower total revenue). If we take Ex 1:

    price x quantity = total revenue

    $450 x 200 = $90,000

    $400 x 300 = $120,000

    While when demand is inelastic, a price cut will decrease total revenue. As in Ex 2:

    $4 x 10 = $40

    $3 x 11 = $33.

    The conclusion is that in terms of machine performance and total revenue, there is a limit to get “improvement”. There is a certain point that we cannot further improve the speed of a machine as well as there is a certain point that we cannot change price to get more total revenue.

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  • CG 12:49 pm on September 4, 2010 Permalink | Reply
    Tags: computer architecture, lab, modelsim, ,   

    Useful link for Computer Architecture lab 

    Great resources and examples

    http://lapwww.epfl.ch/courses/archord1/

     
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