Question #73880

Royal steels Ltd. manufactures metal office furniture with the following production function :
Q = 20K 0.1 L 0.9
The firm currently is producing efficiently using 20 units of capital and 50 units of labor
( a) what is the rate of output ?
( b) What are the relative prices of capital and labor ( i.e., what is the ration of the two input prices?) can u determine the actual price of labor and capital ? Explain
(c) if output sells for Rs. 200 per unit, can you determine the firm's profit? why or why not ?

Expert's answer

Q = 20K^0.1*L^0.9

The firm currently is producing efficiently using K = 20 units of capital and L = 50 units of labor.

(a) The rate of output is:

Q = 20*20^0.1*50^0.9 = 912.44 units.

(b) In equilibrium MPL/w = MPK/k or MPL/MPK = w/k.

MPL = 18K^0.1/L^0.1,

MPk = 2L^0.9/K^0.9,

So, the relative prices of capital and labor are:

w/k = 18K^0.1/L^0.1/ 2L^0.9/K^0.9,

w/k = 9K/L = 9*20/50 = 3.6.

(c) If output sells for Rs. 200 per unit, then we need to know the exact amounts of w and k, so we can't determine the firm's profit.

The firm currently is producing efficiently using K = 20 units of capital and L = 50 units of labor.

(a) The rate of output is:

Q = 20*20^0.1*50^0.9 = 912.44 units.

(b) In equilibrium MPL/w = MPK/k or MPL/MPK = w/k.

MPL = 18K^0.1/L^0.1,

MPk = 2L^0.9/K^0.9,

So, the relative prices of capital and labor are:

w/k = 18K^0.1/L^0.1/ 2L^0.9/K^0.9,

w/k = 9K/L = 9*20/50 = 3.6.

(c) If output sells for Rs. 200 per unit, then we need to know the exact amounts of w and k, so we can't determine the firm's profit.

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