Answer to Question #259450 in Microeconomics for Leah

Question

1. XYZ Co. operates in a competitive market. Its Total Product (Q) is given as Q=f(L)= 3L, and it takes the wage and price as given. Derive the firm's short-run demand for labor as a function of w and p. How much labor will the firm hire if W=₵25 and P=₵150?

2. Show that the quantity of labor(L) and capital(K) that a firm demand decreases with a factor’s own factor price (w for labor and r for capital) and increases with the output price (P) when the production function is a Cobb-Douglas of the form 𝐪 = 𝐀𝐋𝛒𝐊𝛗

Answer 1

Solution:

1.). The short-run labor demand curve is given by MP_L = W / p = w, which is obtained by dividing the nominal demand curve by the product price, p.

MRP_L = w

MP_L $\times$ P = w

MP_L = 3L

P = 150

W = 25

3L $\times$ 150 = 25

450L = 25

L = 0.056

Q = 3L = 3 $\times$ 0.056 = 0.168

Labor = 0.168

2.). A indicates the technology used in the production process. When the value of A is high, the level of output that can be produced by any combination of the outputs is also high.

The Cobb Douglas function given is a homogeneous function and the degree of homogeneity is given by: p and w.

 

From the given equation, when L and K by the factor t, q will decrease by the factor t^p+w.

A decrease in the factor prices of labor and capital will result in more of them being demanded by the firm. Nonetheless, when q decreases by the factor t^p+w, the firm’s demand for the input factors also decreases by the factor t^p+w.