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Economics of Competition and Strategy

ECOS2201

1. Consider a setting with a worker and a firm. The worker can exert an effort level a which is unobservable to the firm and his effort cost is given by Total output is given by y = 20a. The firm offers the worker a take it or leave it wage contract of the form w = s + by. Assume that the firm maximizes profits and the worker maximizes his utility given by The worker’s outside option is u0.

(a) Compute the efficient level of effort. (5 marks)

(b) Set up the maximization problem, where the objective function is written in terms of total surplus, for the firm. That is, write down the objective function, constraints and choice variables for the firm. (5 marks)

(c) Compute the firm’s optimal choice of b and a. (5 marks)

(d) Let u0 = 0. Suppose regulations stipulate that the firm has to set a salary s ≥ 20. Compute the firm’s optimal choice of b, a, and s.(5 marks)

2. Consider a setting with a worker and a firm. The worker exerts an effort level a which is unobservable to the firm and his effort cost is given by C(a) = ca². Total output is given by y = ka + where ϵ is a random variable with E() = 0 and V ar() > 0. Let k = 3 and c = 3.

The firm offers the worker a take it or leave it wage contract of the form w = s+by. Assume that the firm maximizes expected profits, ka−s−bka. Assume that workers, who are risk averse, maximize their certainty equivalent which is given by  where r > 0 is a parameter that measures the degree of risk aversion. The workers outside option is 0.

(a) Compute the efficient level of effort. (5 marks)

(b) Compute the firms optimal choice of b, and a. Using one sentence explain why the effort level is different from that in part (a). (5 marks)

(c) Suppose now, that instead of contracting on output, the firm offers a take it or leave it contract of the form w = s + bp where p = ka + with E() = 0 and V ar() = V > 0. Furthermore, the firm can now choose V by incurring a monitoring cost M(V ) where M is strictly decreasing in V . Rewrite the firm’s optimization problem (using total surplus) and write down the first order conditions (that is, take the first order derivative) with respect to V . Based on this, how does the monitoring intensity (that is measured by how low V is) vary with the level of incentives b? (10 marks)

3. Consider a school district where teachers can engage in two tasks. The first task is to improve test taking skills. The second task is to instill creativity in their students. Let a1 be the teacher’s effort in test taking and a2 be the teachers effort in instilling creativity. Effort is costly for the teacher with the cost function given by

The benefit to a parent from both of these tasks is given by Assume  so that the vector f has a length of 1.

There are three types of parents based on the benefit that they get from these tasks: there are parents who only value test taking, parents who equally value both tasks and, parents who only care about creativity.

The only performance measure available is p = a1 (notice that the vector g = (1, 0) has a length of 1), so that only test taking can be measured. A teacher’s contract takes the form w = s + bp. Assume that the terms of the contract are set by a parent.

(a) For each type of parent specify the optimal level of incentives b. You can do this graphically, using a separate graph for each type of parent. (10 marks)

(b) Specify the total surplus generated from this optimal level of incentives for each type as a function of θ which is the angle between the vectors f and g. You can use the fact that (5 marks)

(c) Consider the type of parent who values each task equally. Suppose this type can modify the performance measure to with  at a cost C. What values of G1 and G2 would this type of parent choose and what is the maximum possible cost they are willing to pay. (5 marks)

4. Consider a partnership with 5 people. All the partners are risk neutral. The output for this partnership is given by y = 4(a1 + a2 + a3 + a4 + a5) where ai is the effort of the i′th partner. Each partner has a cost of effort given by and his outside option is 0.

(a) Compute the efficient level of effort. (5 marks)

(b) Suppose the partners decide to share output equally between themselves. What is the equilibrium level of effort? Compare the answer to the first part.(10 marks)

(c) Show that when each partner posts a bond z up front, they have an incentive to exert the efficient level of effort. Calculate the range in which z must lie. (5 marks)

5. Consider the model of culture in organizations that we covered in class and assume that the organization has a parallel structure where two workers develop projects simultane-ously. Recall that the principal’s payoff from an implemented project is B + β for an implementation of and B for any other implementation. Also recall that worker i’s payoff from an implementation of x is b − |mi − x|.

Consider the following change to this model. Assume that any worker who successfully develops a project can implement it in the organization.

Specifically, for the outcome where both workers are successful, both projects are imple-mented. The principal’s payoff in this case is the sum of her payoffs from both projects. Similarly, a worker’s payoff in this case is the sum of his payoffs from both projects.

(a) Given that each worker choose their ideal implementation when successful, write down worker i’s expected utility at the project development stage for this case. (6 marks)

(b) What is the optimal level of effort for each worker for this case? (6 marks)

(c) Specify the optimal culture of the organization for this case – that is the ideal points of the agents hired. In two sentences explain why this is different from the case where only one project can be implemented. (8 marks)