2.27 The Chuzzlewits have an income of $m per week. Let x be food and let y be a

Question

2.27 The Chuzzlewits have an income of $m per week. Let x be food and let y be all other goods. Let px be the price of food and py be the price of other goods. They can use food stamps to buy food at a price of px(1s) for up to x* units of food per week. If they buy more food than x*, they have to pay the full price, px for additional units. Their weekly income is greater than px(1 s)x. The maximum amount of food that they can buy per week is:

(a) x +(m=px)

(b) (m + x)=px

(c) (m=px)+sx

(d) m=(1 s)px

(e) (m + px)=(1 s)px

answer is c, please show working

Explanation / Answer

It has been provided that family can buy x*units for px(1-s) per unit.

So, they will spend px(1-s)x* on x* units of food.

Weekely income of family = $m

It has been provided that px(1-s)x* is smaller than the weekely income of family.

So,

Remaining income = m - ( px(1-s)x*)

This income can be used to buy more units of food but now each unit of food will cost px per unit.

Additional units purchased = Remaining income/Price of each unit

                                       = [m - ( px(1-s)x*)]/px

Calculate maximum number of food units purchased -

Maximum number = Units purchased with food stamps + Additional units purchased at market price

                           = x* + {[m - ( px(1-s)x*)]/px}

                           = (pxx* + m - pxx* + pxsx* )/px

                           = (m + pxsx*)/px

                           = m/px + sx*

Hence, the correct answer is option (c).

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