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Perhaps some tips on Economics essay?

  • When you press the calculator...
  • I was chatting online with the a senior for some tips. He threw me this essay question:

    "In 2007, the Singapore economy grew at 7.8%, goods and services tax went up from 5% to 7%, and there were active campaigns on healthy living.
    Assess the likely effects of the above changes on consumers' expenditure on fast food."

    Take 5 minutes to plan for an outline. In fact, I suggest MORE than 5 minutes... This was the killer question for last year's promos.

    Ready to see the answer?

    My initial response was:

    talk about demand and supply factor

    economic growth -> increased income
    positive income elasticity -> increased demand

    increased in service tax -> decreased supply
    large extent as supply very price inelastic, tax incidence

    active campaigns -> change in taste of preference
    decrease demand

    conclusion: demand shift less than supply, quantity demanded drops
    _________________

    Looks like a two page, chop chop essay. How wrong was I.

    This senior took 1 hour and 15 minutes to write a 4 page essay on this question. He scored 20/25.

    The key lies in the word EXPENDITURE. EXPENDITURE not QUANTITY DEMANDED or mere CHANGE IN PRICE.

    Expenditure is price times quantity. You are supposed to look at the area under the graph. The emphasis is on the elasticity.

    His other remarkable points:
    Talk about different price elasticities for different income groups
    Campaigns introduces substitutes such as organic food
    Fast food restaurants also coming up with healthy packages
    Ad Valorem tax leads to a PIVOTAL shift, hence making supply more price inelastic
    etc etc...

    Of course, unless you are as god-like as him, it is unwise to burn 1 hour and 15 minutes for an essay. Hope that I post this in time for you guys to warm up (err not fry) your brains.

    Moral of the story: Open your eyes BIG BIG tomorrow

    Cheers,
    Khor Shi-Jie

    Last Minute Mugging...

  • When you press the calculator...
  • Trouble keeping your eyes away from facebook, world cup, etc.? Try using this nifty application:


    Err... well alternatively you can use a stop watch too XD

    Cheers,
    Khor Shi-Jie

    If you hate integration like I do...

  • When you press the calculator...
  • I guess everyone is busy mugging for blocks (and hence the hiatus of the blog ><). But anyway, let me share a shortcut with you guys...

    The killer topic for Math block test is definitely INTEGRATION, and we know it sucks for many reason. The most tormenting part, IMO, must be integration by parts. Personally I hate writing long long expressions, moving bulks of expressions here and there, then end up in a zzz careless mistake.

    Let me introduce a shortcut which is super useful and easy :) This technique is known as tabular integration by parts.

    Suppose you want to solve \int x^3 \cos x \, dx.\! Not an easy task, if you have tried it in your tutorials. In this technique, we still apply LIATE and let u be x^3 and v' be cos x. Now create a table and write:
    Derivatives of u (Column A)Integrals of v (Column B)
     x^3 \, \cos x \,
     3x^2 \, \sin x \,
     6x \, -\cos x \,
     6 \, -\sin x \,
     0 \, \cos x \,

    Such that column A represents the subsequent derivative of u and column B represents the subsequent integrals of v. Repeat this until you can no longer continue, for instance when u arrive at 0. Now, the answer is simply:

    (+)(x^3)(\sin x) + (-)(3x^2)(-\cos x) + (+)(6x)(-\sin x) + (-)(6)(\cos x) + C \,.

    Which is arrived by pairing the 1st term in A with the 2nd term in B , the 2nd term in A with the 3rd term in B, the 3rd term in A with 4th term in B, etc. Take note of the ALTERNATING sign in front of each terms too.

    Another example:

    \int e^x \cos x \,dx.

    Derivatives of u (Column A)Integrals of v (Column B)
     e^x \, \cos x \,
     e^x \, \sin x \,
     e^x \, -\cos x \,


    Then,

     \int e^x \cos x \,dx = e^x\sin x + e^x\cos x - \int e^x \cos x \,dx,

    Which can be solved easily to yield:

    \int e^x \cos x \,dx = {e^x ( \sin x + \cos x ) \over 2} + C\!

    Visit http://en.wikipedia.org/wiki/Integration_by_parts#Tabular_integration_by_parts for more information. My senior used this and saved a lot of time. However, do show your full working still (I can't guarantee that your tutors will accept such cheapskate method). Use it wisely and pwn the block test :P

    Cheers,
    Khor Shi-Jie

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