Consider an economy with three consumers, each with a marginal benefit for a public good of MB = 10–q. If the marginal cost of providing the good is $17 per unit, what is the efficient level of output? [Round your answer to 2 decimal places when needed]
Question
Consider an economy with three consumers, each with a marginal benefit for a public good of MB = 10–q. If the marginal cost of providing the good is $17 per unit, what is the efficient level of output? [Round your answer to 2 decimal places when needed]
Solution 1
The efficient level of output for a public good is determined where the sum of the marginal benefits of all consumers equals the marginal cost of providing the good.
Given that there are three consumers and each has a marginal benefit of MB = 10–q, the total marginal benefit (MB_total) is 3*(10–q).
The marginal cost (MC) of providing the good is given as $17 per unit.
Setting MB_total equal to MC gives the following equation:
3*(10–q) = 17
Solving for q gives the efficient level of output:
30 - 3q = 17 3q = 30 - 17 3q = 13 q = 13 / 3 q = 4.33
So, the efficient level of output is approximately 4.33 units.
Solution 2
The efficient level of output for a public good is determined where the sum of the marginal benefits of all consumers equals the marginal cost of providing the good.
Given that there are three consumers and each has a marginal benefit of MB = 10–q, the total marginal benefit (MB_total) is 3*(10–q).
The marginal cost (MC) of providing the good is given as $17 per unit.
Setting MB_total equal to MC gives the following equation:
3*(10–q) = 17
Solving for q gives the efficient level of output:
30 - 3q = 17 3q = 30 - 17 3q = 13 q = 13 / 3 q = 4.33
So, the efficient level of output is approximately 4.33 units.
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