Suppose a closed economy is populated by two consumers A and B and one firm. The consumers have identical preferences which can be described by a utility function that depends on consumption of good x and leisure l. Each consumer has a fixed amount T = 1 of time available, which can be allocated between leisure and labour supply.

The firm produces consumption good x using labour L as input according to an increasing, concave production function f(L). The firm is owned by consumer A. Assume price taking behaviour of the firm on output and input markets. The output price is denoted by p and wage by w.

a) State all endogenous and exogenous variables.

b) Set up the complete system of equations which determines the equilibrium. Number the equations.

Now assume the government raises a specific tax t on production of good x. The tax gains are fully redistributed to consumer B.

c) State all additional endogenous and exogenous variables.

d) Adjust your system of equations, such that it incorporates the tax