Question

Consider the one-period economy discussed in class. Suppose the utility function of the representative consumer is given by U(C,l)=γlogC+(1−γ)logl where 0<γ<1,C is a bundle of consumption goods and l is leisure. The consumer maximizes U(C,l) subject to the budget constraint and the time constraint. Firms choose labour to maximise profits subject to the technological constraint Y=zN d

. As first step suppose that to finance the government spending G, the government uses lump-sum taxes. (a) (10 points) Determine firm's labour demand curve and plot it. Find firm's profits.

Answer 1

The labor demand curve for the firm can be determined by analyzing profit-maximizing behavior. The curve is downward sloping, showing the relationship between the wage and the level of labor demanded by the firm.

Step-by-step explanation:

The labor demand curve for the firm can be determined by analyzing the profit-maximizing behavior of the firm. To do this, we need to find the level of labor that maximizes the firm's profits. The firm's profit function is given by π = Y - wN, where Y is the firm's output, w is the wage, and N is the level of labor. To maximize profits, the firm chooses the level of labor that equates the marginal revenue product of labor (MRP) to the wage. Mathematically, this can be represented as MRP = w.

Now, let's plot the labor demand curve. The labor demand curve shows the relationship between the wage and the level of labor demanded by the firm. As the wage increases, the firm will demand less labor, and as the wage decreases, the firm will demand more labor. The labor demand curve is downward sloping. The profit-maximizing level of labor for the firm can be found by solving MRP = w for N. Once we find the level of labor, we can plug it into the profit function to calculate the firm's profits.