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Summary TUTORIAL 8A QUESTION PAPER

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Master STK120 with Confidence! Stressed about acing your STK120 exams and tests? We've got the ultimate study pack to boost your understanding and exam performance. Our comprehensive collection of past STK120 tutorial papers and detailed memos provides valuable insights into exam format, key c...

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TUT8A Exercise 5 memo
A coffee shop on campus uses paper coffee cups. The relationship
between the demand, 𝑞 in 100s , of paper coffee cups and the price,
𝑝(in R1000), is given by:
𝒍𝒏 𝟒𝒒 𝟏
𝒑 𝒈 𝒒 𝟐
, 𝟏 𝒒 𝟗𝟎
𝒒
Hint: Income = Demand x Price
1. Calculate and interpret the marginal rate at which the price will change, if the
demand is 300.
𝟒
𝒒𝟐 𝟐𝒒𝒍𝒏 𝟒𝒒 𝟏
𝟒𝒒 𝟏
𝒈 𝒒
𝒒𝟒
𝟒 𝟑 𝟐
𝟐 𝟑 𝒍𝒏 𝟒 𝟑 𝟏
𝟒 𝟑 𝟏
𝒈 𝟑 𝟒
𝟎. 𝟏𝟓𝟓𝟖𝟎𝟖 ∗ 𝟏𝟎𝟎𝟎 𝑹𝟏𝟓𝟓. 𝟖𝟏
𝟑
Price will decrease with R155.81 if the demand increases from 300 to 400 cups
2. Give the income function and units that income is measured in.
𝒍𝒏 𝟒𝒒 𝟏 .𝒒 𝒍𝒏 𝟒𝒒 𝟏
Income function: 𝑰 𝒒 𝒑𝒒
𝒒𝟐 𝒒
1
The units that income is measured in, is: 𝑹𝟏𝟎𝟎𝟎 ∗ 𝟏𝟎𝟎 𝑹𝟏𝟎𝟎 𝟎𝟎𝟎

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