To find the consumer optimum, we need to compare the marginal utility per dollar spent on each app. We calculate this by dividing the marginal utility of each app by its price.
For the sports app:
Marginal utility per dollar = Marginal utility / Price = 1200 / $2 = 600 utils per dollar
For the game app:
Marginal utility per dollar = Marginal utility / Price = 1700 / $1 = 1700 utils per dollar
Now, we need to compare the marginal utility per dollar for each app and allocate the available budget accordingly. Since the game app offers a higher marginal utility per dollar, the student should allocate more of her budget towards the game app.
Let's calculate how many game apps she can afford with her budget of $9 per week:
Game apps affordability = Budget / Price = $9 / $1 = 9 game apps
Now, let's compare the marginal utility for the 9th game app and the marginal utility for the 6th sports app:
Marginal utility of 9th game app = 200
Marginal utility of 6th sports app = 200
Since both have the same marginal utility, our consumer optimum will be to purchase 6 sports apps and 9 game apps.
Therefore, the student will purchase 6 sports apps and 9 game apps. Her consumer utility will be the sum of the marginal utilities of those apps:
Consumer utility = (1200 + 1000 + 800 + 600 + 400 + 200) + (1700 + 1400 + 1100 + 800 + 500 + 200)
Consumer utility = 5400 + 4600
Consumer utility = 10000 utils
Quantity of Sports Appper Week: 1, 2, 3, 4, 5, 6
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 $2 per week, the subscription price of a game app is $1 per week, and a student has $9 per week to spend on these two items, at a consumer optimum she will purchase ---sports apps and---game apps. Consumer utility will be ---utils.
1 answer
1 answer