Reference no: EM132767610
Question - An agency's manager can put high, medium, or low effort into cost-minimization. High effort will limit the agency's operating costs to $100,000. However, high effort costs the manager the equivalent of $20,000. Low effort will increase the agency's operating costs up to $200,000. However, low effort costs the manager nothing. Medium effort leaves the agency's operating cost uncertain. There is an 80% chance that the manager will be "lucky" and agency costs will only be $100,000. But there is a 20% chance that the manager will be "unlucky" and agency costs will rise to $200,000. Medium effort costs the manager the equivalent of $10,000.
1) What is the total cost (the sum of the agency's operating cost and the manager's effort cost) if the manager exerts high effort?
2) What is the total cost (the sum of the agency's operating cost and the manager's effort cost) if the manager exerts low effort?
3) What is the total expected cost (the sum of the agency's expected operating cost and the manager's effort cost) if the manager exerts medium effort?
4) What is the economically efficient effort level?
a. High effort
b. Low effort
c. Medium effort
The manager rationally chooses low effort if paid a base salary that is independent of performance. In that case, the agency's operating costs are $200,000 and the manager pays no effort cost, so total costs are $200,000. A bonus tied to operating costs could incentivize the manager to choose the efficient outcome, while reducing the agency's operating costs (including any bonus payments). But the bonus has to be well-designed in order to be mutually beneficial for both the manager and agency. Suppose that the manager is offered a $45,000 bonus if operating costs are low. High effort, with an effort cost of $20,000, guarantees that operating costs will be low and that the bonus is received. Medium effort, with an effort cost of $10,000, has an 80% chance of yielding low operating costs and therefore an 80% chance that the bonus is received. Low effort, with an effort cost of $0, has no chance of yielding low operating costs and therefore no chance that the bonus is received.
5) What is the manager's gain (bonus minus effort cost) from high effort?
6) What is the manager's expected gain (expected bonus minus effort cost) from medium effort?
7) What effort level does the manager choose if offered a $45,000 bonus?
a) High effort
b) Medium effort
8) What are the agency's costs, inclusive of any expected bonus payments, if it offers a $45,000 bonus for low operational costs?
Suppose that the manager is instead offered a $55,000 bonus if operating costs are low. High effort, with an effort cost of $20,000, guarantees that operating costs will be low and that the bonus is received. Medium effort, with an effort cost of $10,000, has an 80% chance of yielding low operating costs and therefore an 80% chance that the bonus is received. Low effort, with an effort cost of $0, has no chance of yielding low operating costs and therefore no chance that the bonus is received.
9) What is the manager's gain (bonus minus effort cost) from high effort?
10) What is the manager's expected gain (expected bonus minus effort cost) from medium effort if offered a $55,000 bonus for low operating costs?
11) What effort level does the manager choose if offered a $55,000 bonus?
a. High effort
b. Medium effort
12) What are the agency's costs, inclusive of any expected bonus payments, if it offers a $55,000 bonus for low operational costs?