A local snowboard firm wants to produce 200 snowboards next month. The firm must

Question

A local snowboard firm wants to produce 200 snowboards next month. The firm must hire more labor in order to produce at this level (Q=200), and is faced with the option of hiring either skilled or unskilled workers (denoted by S and U, respectively). Should the firm hire always hire the most skilled workers? Under what conditions would the firm hire unskilled workers? Under what conditions would the firm hire skilled workers? Please formally derive your conclusions.

Assume the following:

Production Function: Q=aS+U

Total Cost = W sS +WuU

Ws= wage of skilled workers

Wu= wage of unskilled workers

Now assume that Ws = 10, Wu = 8 and a = 2. Would the firm hire more skilled or unskilled workers? Explain.

Explanation / Answer

Q = aS + U

TC = WsS + WuU

The firm will choose that combination of skilled & unskilled labor for which,

MPS / MPU = wS / wU

Or,

Slope of isoquant (Representing production function) = Slope of total cost line (Isocost)

Here, MPS = dQ / dS = a

MPU = dQ / dU = 1

So, the optimality condition will be

a / 1 = Ws / Wu

Or, Ws = a x Wu

If a = 2, Ws = 10 & Wu = 2,

Ws / Wu = 5

And

200 (Q) = 2S + U

MPS = dQ / dS = 2

MPU = dQ / dU = 1

So, (MPS / MPU) = 2 & (Ws / Wu) = 1.25

(MPS / MPU) > (Ws / Wu)

So, firm should hire more unskilled labor.

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