## 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?

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?

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.