Questions: Given the following table, fill in the blank below. Price of Pizza = 5 Price of Video = 4 Price of Video = 5 MU/ Videos Units Total Utility Pizzas MU/ Pizzas Total Utility Videos MU/ Videos 1 50 10 30 7.5 6 2 90 8 58 7 5.6 3 120 6 82 6 4.8 4 140 4 102 5 7 5 150 2 118 4 3.2 6 155 1 130 3 2.4 7 155 0 138 2 1.6 If your income was 40 and the price of pizzas was 5 and the price of videos was 4, what combination of pizzas and videos would maximize your utility? A. 3 of each. B. 4 pizzas and 2 videos. C. 5 pizzas and 4 videos. D. 4 pizzas and 5 videos. Now your income is still 40 but the price of videos increased from 4 to 5.

To determine the combination of pizzas and videos that maximizes utility given the budget constraint, we need to consider the marginal utility per dollar (MU/$) for each item and the total cost of the combinations.

Initial Prices:

• Price of Pizza = $5
• Price of Video = $4
• Income = $40

MU/$ Calculation:

• For pizzas, the MU/$ is given directly in the table.
• For videos, the MU/$ is also given in the table.

Budget Constraint:

• Total cost = (Number of Pizzas × $5) + (Number of Videos × $4) ≤ $40

Options: A. 3 pizzas and 3 videos:

• Cost = (3 × $5) + (3 × $4) = $15 + $12 = $27
• MU/$ for 3 pizzas = 6, MU/$ for 3 videos = 6

B. 4 pizzas and 2 videos:

• Cost = (4 × $5) + (2 × $4) = $20 + $8 = $28
• MU/$ for 4 pizzas = 4, MU/$ for 2 videos = 7

C. 5 pizzas and 4 videos:

• Cost = (5 × $5) + (4 × $4) = $25 + $16 = $41 (exceeds budget)

D. 4 pizzas and 5 videos:

• Cost = (4 × $5) + (5 × $4) = $20 + $20 = $40
• MU/$ for 4 pizzas = 4, MU/$ for 5 videos = 4

Analysis:

• Option A: Total cost is $27, and the MU/$ is balanced at 6 for both items.
• Option B: Total cost is $28, with a higher MU/$ for videos (7) than pizzas (4).
• Option C: Exceeds budget, not feasible.
• Option D: Total cost is $40, with equal MU/$ of 4 for both items.

Conclusion: The answer is D: 4 pizzas and 5 videos. This combination uses the entire budget and balances the marginal utility per dollar spent on both pizzas and videos.

Price Change: Now, the price of videos increases to $5. We need to re-evaluate the options with the new price constraint.

New Budget Constraint:

• Total cost = (Number of Pizzas × $5) + (Number of Videos × $5) ≤ $40

Re-evaluate the feasible combinations with the new price of videos:

• Option A: 3 pizzas and 3 videos

  • Cost = (3 × $5) + (3 × $5) = $15 + $15 = $30
  • MU/$ for 3 pizzas = 6, MU/$ for 3 videos = 6

• Option B: 4 pizzas and 2 videos

  • Cost = (4 × $5) + (2 × $5) = $20 + $10 = $30
  • MU/$ for 4 pizzas = 4, MU/$ for 2 videos = 7

• Option C: 5 pizzas and 4 videos

  • Cost = (5 × $5) + (4 × $5) = $25 + $20 = $45 (exceeds budget)

• Option D: 4 pizzas and 5 videos

  • Cost = (4 × $5) + (5 × $5) = $20 + $25 = $45 (exceeds budget)

With the new price, options C and D exceed the budget. Therefore, the best option is A: 3 pizzas and 3 videos, which maximizes utility within the budget constraint.