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# Beliefs and payout structure

Question 1 a)
Assume that we are in an economy with two-workers and one firm. One worker is of average ability, with Marginal Product = 10 and cost of education function C(S)= 3S. The other worker is high-ability with Marginal Product = 15 and C(S) = S/2 . After high school, both workers must choose how much education to pursue, anywhere between 0 to a maximum of 6 years (S = {0,1,2,3,4,5,6}). The firm has the following perceptions of worker ability, with the associated pay structure:
If S < 4 then MP = 10 & w = 10
If S ≥ 4 then MP = 15 & w = 15
That is, if the employer sees less than 4 years of education they assume they are looking at someone of average ability and will pay them a wage equal to the average- ability marginal product. If they see 4 or more years of education, they assume they are looking at someone of high ability and will pay them a wage of \$ 15. Given these beliefs and payout structure, how many years of education will each ability-type pursue and what will their pay be?
Question 1 b)
To increase the number of years people of average ability spend in post-secondary education, the federal government proposes reducing their cost of schooling by 1/3. This transforms the average ability cost of education function into C(S) = S. Is it now optimal for those of average ability to pursue 4-years of education?
Question 2 c)
In an effort to bring in more educated workers, the firm updates its belief and payout structures in the following fashion:
If S < 2 then MP = 10 & w = 10
If S ≥ 2 & S < 5 then MP = 15 & w = 15
If S ≥ 5 then w = 20
That is, if the firm sees at least 5 years of education, they will choose to pay w = 20 regardless of the workers Marginal Product. Given this belief structure, and assuming that the cost functions of education take on the same form that they had in part a), how many years of education will those of average ability and high ability pursue and what will be their respective wage rates.
Question 1 d)
To reduce the cost burden of education, the government divides each persons cost function in half. For those of average ability, their cost function now looks like C(S) = 3 2S, and for those of high ability it is now C(S) = S/4 . On top of this, the firm also retains the same belief structure as in part c),
If S < 2 then MP = 10 & w = 10
If S ≥ 2 & S < 5 then MP = 15 & w = 15
If S ≥ 5 then w = 20
Given this, how many years of education will both types pursue and what will be their respective payouts?

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