2. (4 points} Consider the signaling theory covered in class. Assume that there are two types of workers: Type L (\"low productivity") and Type H (\"high productivity\"}. Each worker can obtain 5: units of education at a cost. For each worker type. its marginal product of labor and cost of acquiring education are as follows: _ Mar_inal .roduct of labor Cost of 3 units of education 2s + 1.255 The rm cannot observe each worker's true type. However. it can observe how many units of education each worker has acquired. Assume that if the rm observes that a worker has s* or higher units of education. the rm believes that they are Type H [regardless of whether the worker*s true type is Type H or not}. The rm pays wages based on the rm's belief of their type. Assume that the rm operates in a perfectly competitive market and their output price is p=l. For each worker, dene their payoff as [wages cost of .9 units of education} with I} 5 s 5 2!] (think of s=l 6 being college education}. a} (I point) For each worker type. write down their payoffs for each of these two cases: Case {i}: Ifssis" Case {ii}: Ifs 3: s* Your answer should be expressed in terms of s. For each worker type and each case described in part a]. briey explain what each worker's optimal units of education would be. h} (I point) Based on your answers from part {a}1 derive the range of s* in which a separating equilibrium will occur. c} (fleeing) 1|What isthe range ofs* in which a pooling equilibrium will occur'? Eriey explain. d} (I point) Based on your answers in parts {a} to (c). what value should the rm set s* to'? Explain