Question

The manager of a 100-unit complex knows from experience that all units will be occupied if the rent is $700 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue? Assume the demand function is linear. Remember to justify your answer.

Answer 1

To maximize revenue, the manager should charge a rent of $710 per month.

Step-by-step explanation:

To maximize revenue, the manager should find the rent at which the number of units rented multiplied by the rent is the highest. Let's calculate the rent that will maximize revenue using the given information:

1. At a rent of $700 per month, all 100 units are occupied. So, the revenue for this rent is $700 x 100 = $70,000.
2. For every $10 increase in rent, one additional unit will remain vacant. So, for a rent of $710 per month, 99 units will be occupied, and the revenue will be $710 x 99 = $70,290.
3. This process can be continued to find the revenue for different rents, and we can conclude that as the rent increases, the revenue also increases.
4. The rent that maximizes revenue can be found by plotting the data points and finding the highest point on the graph.

Based on this information, the manager should charge a rent of $710 per month to maximize revenue.