• the problem of Firms

Firms in this economy are competitive. They seek to maximize their profits. To do this, they produce Yst units of goods and services that they offer on the goods and services market, using three production factors: the labor demanded in quantity Ldt on the labor market at each date t paid at real hourly wage rate wt, the capital which belongs to them and which is used at full capacity Kt at each date t and the land or land, which is rented to the landowning households for a quantity Tdt at each date t, at the rate hourly rental rate (land rent rate) Rt.

1-Write the maximization problem of the firm representative of the economy

2-Write the first order conditions and interpret them properly.

*Be careful to adapt your interpretation sentence to this new context, where the firm now simultaneously chooses two factors of production.

3-Deduce from Euler's Theorem (applied here on 3 variables) the level of equilibrium profits