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For the economy below, formulate the equilibrium conditions and the social planner problem: Suppose there are a consumer and a competitive firm in the economy

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For the economy below, formulate the equilibrium conditions and the social planner problem: Suppose there are a consumer and a competitive firm in the economy. Consumer preferences depend on leisure I and consumption c: u(c, 1) = c5 15. In addition, she obtains income from owning K units of capital and working in the firm. Consumer is the owner of the firm. The firm produces consumption good c from labor and capital rented in the market. Production technology is c= K 0.25 10.5.