you are a manager for herman millera major manufacture of of

you are a manager for herman miller-a major manufacture of office furniture. you recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevan production function is

Q=2(K)1/2(L)1/2

where K represents capital equipment and L is labor. Your company has already spent a total od $10.000 on the 4 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility nedeed to acquire additional equipment. if workers at the firm are paid a competitive wage of $100 and chairs can be sold for @200 each, what is your profit maximizing level of output and labor usage? what is your maximum profit?

Solution

Since capital cannot be changed, it becomes a question of short run. In short run, we can find the optimum level of labour to be used by formula: MRP = MRC where MRP = Marginal Revenue of labor (MR_L) * Price of the product and MRC = wage rate of the labor.

MR = (2K^1/2 )* 0.5* L^{-1/2 =} K^1/2/ L^1/2 and P = 200 . So MRP = 200 K^1/2/ L^1/2

MRC = 100

Now MRP = MRC

200 K^1/2/ L^1/2 = 100, Solving this gives L = 4K.

K is given as fixed 4, so L = 4*4 = 16 units.

Now with L = 16 and K = 4, we can calculate

Q =2 K^1/2/ L^1/2

Q = 2*2*4 = 64 units.

Reveue from selling 64 units = 64* 200 = 12800

total cost = 10000 + 16*100 = 11600

Profit = 12800-11600 = 1200$