Question

Suppose that as a consumer you have $34 per month to spend on munchies—either pizzas, which cost $6 each, or Twinkies, which cost $4 each.

Create a set of marginal utility tables for each product, like the ones below. Remember that they must show diminishing marginal utility as more of each product is consumed.

Create the corresponding set of total utility tables for each product.

Graph the budget constraint with Pizzas on the horizontal axis and Twinkies on the vertical axis. What are the intercepts? Can you express the budget constraint as an algebraic equation for a line?

# of Pizzas	1	2	3	4	5	6	7
Marginal Utility
Total Utility

# of Twinkies	1	2	3	4	5	6	7
Marginal Utility
Total Utility

Should you purchase a Twinkie first or a Pizza first to get the “biggest bang for the buck”? How can you tell? What should you purchase second, third, etc. until you exhaust your budget?

Confirm that the combination of Twinkies and Pizzas you end up with will maximize your total utility by computing the total utility from other points on the budget line and comparing them to what you chose.

Answer 1

8# of Pizzas	1	2	3	4	5	6	7
Marginal Utility	20	18	16	14	12	10	8
Total Utility	20	38	54	68	80	90	98

# of Twinkies	1	2	3	4	5	6	7
Marginal Utility	10	9	8	7	6	5	4
Total Utility	10	19	27	34	40	45	49

X-intercept: 34/6 = 5.67 (Represents the maximum number of pizzas you can buy if you spent all the income on pizza)
Y-intercept: 34/4 = 8.5 (Represents the maximum number of Twinkies ou can buy if you spent all the income on Twinkies)

Budget constraint: 34 = 6x + 4y
So y = 8.5 - (6/4)x

Marginal Utility of First Pizza/Price of Pizza = 20/6 = 3.33
Marginal Utility of First Twinkie /Price of Twinki = 10/4 = 2.5
Thus, consume pizza first.

Marginal Utility of Second Pizza/Price of Pizza = 18/6 = 3
Marginal Utility of First Twinkie /Price of Twinki = 10/4 = 2.5
Pizza should be consumed second also.

Marginal Utility of Third Pizza/Price of Pizza = 16/6 = 2.67
Marginal Utility of First Twinkie /Price of Twinki = 10/4 = 2.5
Pizza should be consumed third also.

Marginal Utility of Fourth Pizza/Price of Pizza = 14/6 = 2.33
Marginal Utility of First Twinkie /Price of Twinki = 10/4 = 2.5
Twinki should be consumed fourth

Marginal Utility of Fourth Pizza/Price of Pizza = 14/6 = 2.33
Marginal Utility of Second Twinkie /Price of Twinki = 9/4 = 2.25
Pizza should be consumed fifth.

Marginal Utility of fifth Pizza/Price of Pizza = 12/6 = 2
Marginal Utility of Second Twinkie /Price of Twinki = 9/4 = 2.25
Tinkie should be consumed sixth

Total Expenditure = (4 x 6) + (2 x 4) = $32
Now cannot make any more purchases.

Thus, optimum bundle is 4 pizza and 2 twinkies.