Question

Suppose the representative firm’s production function is Y = zK 0.5N 0.5 .

A. Find the marginal product of labour. Are there diminishing returns to labour?

B. If the real wage paid to labour is w, determine the representative firm’s demand for labour (Nd ) as a function of w, A and K, assuming the firm maximizes profit.

C. Find and interpret the following derivatives: (∂N d /∂w), (∂N d /∂z), (∂Nd /∂K).

D. Draw rough graphs to explain what your derivatives are showing.

Answer 1

0.5-1 es -09 dro Production function : Y= 2K 005 I A Marginal product of labor pros N - ZK (0.510 oosy, merginel product [men 20.52 (2) man labor checking returns to labor dme = (0.5) 2 (-0.57 K 215<0 . So, It shows that there is diminishing retums to labor. Bil : At profit maximization MPN = w 0.5 -115 6.5 0.52/K ) = w . 0.5 . 0.52 (kjo's anos (0.5 z (klos an 10:25 2 ² K = Ni 7 firm's demand for 0, labor I c dw an = 0.25 2² K (-2) (wyko It implies labor demand falls with increase in reel wage. 2 = 0.25 (22) Ķ2 70 22 It implies labor demand increases with increase in z(poductivity) labor demand increases with increase in capitalo

de figuret? Law and not a showing 2 w To > N demand for labor falls as w increeses ..[figure 2] . Es t - bol z demand for labor increeses with increase in productivity (2). [figure 3] demand for labor increase, with increase in egital (K).