Consider an economy with two individuals, agent 1 and agent 2, as well as a

government. The two agents value consumption goods and leisure. The preferences of agent 1 are captured

by the utility function U(C1,L1) = 2C1L1, where C1 denotes consumption of agent 1 and L1 denotes leisure of agent 1. Similarly, the preferences of agent 2 are captured by the utility function U(C2,L2) = 2C2L2,

where C2 denotes consumption of agent 2 and L2 denotes leisure of agent 2.

Each agent allocates their time between leisure and education (for simplicity, we do not model the decision

about how much to work after receiving an education). The resource constraint of agent 1 is L1 +E1 = 100,

where E1 denotes the level of education of agent 1. Similarly, the resource constraint of agent 2 is L2+E2 =

100, where E2 denotes the level of education of agent 2.

The more education an agent acquires, the more the agent will shift the technological frontier of the society

outward (better iPads and better medicines!). We denote the quality of technology by A and assume that

the quality of technology is given by expression A = E1 + E2:

Each agent's consumption is determined by the agent's own production and government transfers to the

agent. Agent's own production in turn depends on the agent's own level of education and on the quality

of the available technology (more educated individuals are better positioned to take advantage of the newly

developed technologies than less educated individuals). Formally, we assume that C1 = 2E1 +A+S1, where

S1 is a government transfer to agent 1, and 2E1+A is production of Agent 1, and C2 = 2E2+A+S2, where

S2 is a government transfer to agent 2, and 2E2 + A is production of Agent 2.

For analytical simplicity, we assume that each agent can choose either a low level of education, 40, or a high

level of education, 70

We assume that the government transfer to an agent depends on the agent's choice of education level. Each

individual who selects the high education level receives a subsidy Si = 20. Those who select the low education

level receive no transfer from the government. The individuals choose their education levels simultaneously

and non-cooperatively.

a) Solve for the best responses.

b) Determine each agent's utility in the Nash equilibrium.