Question

Describe all the conditions that must be satisfied in the one-period macroeconomic model for there to be a competitive equilibrium.

Answer 1

The conditions that must be satisfied in the one-period macroeconomic model for there to be a competitive equilibrium are described as follows:

1. Optimization for the consumer: To maximize his utility, the consumer in this model chooses his budget constraint, denoted as C and supply of labor, denoted as N^s . The utility function takes the form,

                           Maximize U(C, N^s)

                          subject to the constraint, C= w*N^s + - T

where, w= hourly wage rate of the consumer; = profits earned by the consumer who owns the firm; T= taxes paid by the consumer.

2. Optimization for the firm: To maximize its profits, the firm in this model chooses its demand for labor, denoted as N^d. The profit function takes the form,

                            Maximize (Y, N^d)

                        subject to the constraint, Y= z* F(K,N^d)

where, Y= production of this firm; z= total factor productivity; K= quantity of capital used as input by this firm.

3. The labor market is at equilibrium, that is the demand for labor equals the supply of labor

                                  or, N^d = N^s

4. The Government in this model spends off all their revenue because there is no future period to save, since after all it's one-period model. Also the Government cannot borrow any money from anyone as debt, to be repaid in future, again because it's a one-period model where there is no concept for future.

Thus, government expenditure (G) is equal to taxes earned (T) or this model or simply G = T.