Question

Quantity of Corn Total Utility Marginal Utility Quantity of Steaks Total Utility Marginal Utility

1

16

16 1 30 30
2 30 14 2 46 16
3 42 12 3 61 15
4 52 10 4 75 14
5 60 8 5 88 13
6 66 6 6 100 12
7 70 4 7 111 11
Your family is deciding how much corn and steak to purchase for a 4th of July picnic. You and your family decide to make a utility schedule which appears above. If the price of corn is $1 and price of a steak is $1, how many steaks should your family purchase for their 4th of July picnic if you have a budget of $6?

Answer 1

The first case the expenditure is under budget whereas in the third case the expenditure is over budget. The budget is only met in the case 2. Therefore the family should purchase 4 steaks and 2 corns.

Step-by-step explanation:

As the values of the table are not clear, by searching for the question the data is found which is as attached with the question.

Now As the price of both the corn and steak is 1 so the values of Marginal Utility over price will remain same as given in the attached table.

In order to maximize the marginal utility over expenditure(price) , the cases are required where value of marginal utility over expenditure for corn and steak is same.

Thus following 3 cases will maximize the marginal utility over expenditure.

Case No 01: For the Marginal Utility over Expenditure of 16

n_c1=Units of Corn=1

n_s1=Units of Steak=2

Case No 02: For the Marginal Utility over Expenditure of 14

n_c2=Units of Corn=2

n_s2=Units of Steak=4

Case No 03: For the Marginal Utility over Expenditure of 12

n_c3=Units of Corn=3

n_s3=Units of Steak=6

Now as the constraint of budget exists as $6 so the expenditure for all the cases is calculated as below:

Case 01 : With 1 unit of Corn and 2 units of Steak

Expense is given as

`Expense_1=Price_c* n_(c1)+Price_s* n_(s1)\\Expense_1=\$1* 1+\$1* 2\\Expense_1=\$3`

Case 02 : With 2 units of Corn and 4 units of Steak

Expense is given as

`Expense_2=Price_c* n_(c2)+Price_s* n_(s2)\\Expense_2=\$1* 2+\$1* 4\\Expense_2=\$6`

Case 03 : With 3 units of Corn and 6 units of Steak

Expense is given as

`Expense_3=Price_c* n_(c3)+Price_s* n_(s3)\\Expense_3=\$1* 3+\$1* 6\\Expense_3=\$9`

So in the first case the expenditure is under budget where as in the third case the expenditure is over budget.

The budget is only met in the case 2.

Therefore the family should purchase 4 steaks and 2 corns.