Quantity of Sports App per Week: 1, 2, 3, 4, 5, 6

Question

Marginal Utility of Sports App: 1200, 1000, 800, 600, 400, 200
Quantity of Game App per Week: 1, 2, 3, 4, 5, 6
Marginal Utility of Game App: 1700, 1400, 1100, 800, 500, 200

Refer to the table above. If the subscription price for a sports app is ​$1 per​ week, the subscription price of a game app is ​$2 per​ week, and a student has ​$13 per week to spend on these two​ items, at a consumer optimum she will purchase---sports apps and--- game apps.

Answer 1

To determine the consumer's optimum, we need to compare the marginal utility per dollar of each app. This can be found by dividing the marginal utility of each app by its respective subscription price.

For the sports app:
- Marginal utility per dollar for 1 sports app: 1200/1 = 1200
- Marginal utility per dollar for 2 sports apps: 1000/2 = 500
- Marginal utility per dollar for 3 sports apps: 800/3 ≈ 267
- Marginal utility per dollar for 4 sports apps: 600/4 = 150
- Marginal utility per dollar for 5 sports apps: 400/5 = 80
- Marginal utility per dollar for 6 sports apps: 200/6 ≈ 33.33

For the game app:
- Marginal utility per dollar for 1 game app: 1700/2 = 850
- Marginal utility per dollar for 2 game apps: 1400/4 = 350
- Marginal utility per dollar for 3 game apps: 1100/6 ≈ 183.33
- Marginal utility per dollar for 4 game apps: 800/8 = 100
- Marginal utility per dollar for 5 game apps: 500/10 = 50
- Marginal utility per dollar for 6 game apps: 200/12 ≈ 16.67

Considering the student has $13 per week to spend, let's calculate the maximum number of apps the student can purchase for each:

For sports apps:
- $1 per sports app
- $13 budget
- Maximum sports apps = $13 / $1 = 13

For game apps:
- $2 per game app
- $13 budget
- Maximum game apps = $13 / $2 = 6.5 (round down to 6)

Comparing the marginal utility per dollar, the consumer optimum is to purchase:

- Sports apps: 6 apps (maximum affordability)
- Game apps: 6 apps (maximum affordability)

Therefore, at the consumer optimum, the student will purchase 6 sports apps and 6 game apps.