Answer should be typed.

how can i solve this problem? especially (a) and (b). (c) and (d) if possible. 6. A worker with a marginal value product of 0 can earn w, = kv0 in self- employment. Marginal value products vary across the population according to the uniform distribution, i.e., 0 ~ U [0, 2]. Firms cannot measure individual productivity, so all workers are paid a wage equal to the average of the marginal value products of those employed. Find the condition for k under which every worker will choose self- employment. Also, find the condition for k under which all the workers will choose to be employed. Assume that k = 1. And, each worker can take a free test which can only tell whether his marginal value product is in [0,1] or in [1,2]. Who will take the test and who will not? Also, who will be self-employed and who will be employed? (c) Assume that k = 1. And, each worker can take a test at the expense of c which can reveal his marginal value product exactly. Who will take the test and who will not? Also, find the condition for c under which there exist some workers who will choose to take the test. (d) Continuing from (c), the test is not perfect in the sense that if a worker with 0 takes the test, the test reveals that the worker's marginal value product is 0 + d with probability 1/2 and 0 - d with probability 1/2. Will more or less workers take the test than in (c)? (Hint: After the test result is revealed, each worker can decide whether to be self-employed or employed.)