# What will be the choice of type 1 agents of type 2 agents?

The population of workers is composed of two types of agents type 1 agents and type 2 agents with 3 Show more The population of workers is composed of two types of agents type 1 agents and type 2 agents with 3/4 of type 1 agents and 1/4 of type 2 agents. Type 1 agents are less productive than type 2 agents and education is more costly for type 1 agents than for type 2 agents. More specifically the productivity of each type of agent (i.e the value of what they can produce in a year) is F1 = 15 F2 = 30 where all the numbers are in thousands. The cost of acquiring the level of education e is c1(e) = 4e for a type 1 agent and c2(e) = 2e for a type 2 agent so that the utility function of a type i agent receiving a wage of w and investing in e units of education is ui(w e) = w ci(e) i = 1 2 There are plenty of firms employing these workers. When a worker applies for a job in a firm the firm cannot tell if he/she is a type 1 or a type 2 agent. All that a firm can observe is the level of education of the applicant. (a) Draw the indifference curves of an agent of type 1 through the points (150) (w = 15 e = 0) through the point (15 3) through the point (30 3) through the point (30 6) through the point (3010). 1 (b) On the same graph draw the indifference curves of an agent of type 2 through the same points. (c) Suppose firms propose the following wage schedule to job applicants w(e) = 15 if e < 6 w(e) = 30 if e 6 What will be the choice of type 1 agents of type 2 agents? It will be cleaner to use a new graph to draw the wage schedule and the indifference curves of the two types of agents to illustrate your answer. Is this wage schedule a Spence equilibrium? (d) Suppose the wage schedule is w(e) = 15 if e < 3 w(e) = 30 if e 3 Answer the same questions as in (c). Show less

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