Question

Assume a 5-member household with a monthly income of $6000. This household allocates its income to the purchasing of food and non-food products. If the average price of food products is $30 per unit and nonfood items cost $120 per unit

(a)Write the household budget equation.

(b) If this household purchases 100 units of food products each month, how many units of nonfood items it can buy?

(c) Assume that the household's allocation of its monthly budget to nonfood products is 5 times that of its budget allocation for food. What is this household optimal bundle?

(d) Assume the price of food products increases to $35 per unit. Write the household's new budget equation. If this household wants to purchase quantities of food and nonfood items in the same proportion as in part (c), what is the household's new bundle?

(e) Assume the price of food products increases to $35 per unit. If this household wants to maintain its allocation of budget to purchase of food and nonfood items in the same proportion as in part (c), what is the household's new bundle?

Answer 1

per product cost of Food Items=30

Per unit cost of Non Food Items=120

1)

Let Total Food Items Purchased = X

Let Total Non Food Items Purchased=Y

Total Spending=6000

So, Budget Equation will be=

30X+120Y=6000

2)

In Part 2,it is given that total food items purchased is 100 units putting it in budget equation

30*100+120*Y=6000

120*Y=6000-3000

120*Y=3000

Y=3000/120=25

3)

Allocation of Non Food items to Food items is 5:1

Total budget=6000

So, 5x+x=6000

6x=6000

x=1000

Budget for Non food items=5*1000=5000

budget for Food items=1000.

Household can purchase max 33 units of Food items and 41 units of Non food items from the given allocation.

Optimum Bundle will be calculated on the bases of Utilities given by each unit. the combination which provide the maximum utility will be the optimum bundle.

say, If no food item is purchased then non food items purchased that can be purchased will be=6000/120=50.

and, if no non food item is purchased then the food items can be purchased will be=6000/30=200.

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4)

So, if the price of food items increased to $35

and other factors being constant

the new equation will be

35X+120Y=6000.

if food items purchased is 120 then Non food items purchased will be 6000-4200/120=15.

5)

if allocation is same 1000 for food items and 5000 for non food items then

Max food items can be purchased will be 28 and non food items that can be purchased will be 5000/120=41 units.