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
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
