- Essay Question: Assume a firm uses two inputs in its production process: labou

Question

- Essay Question:

Assume a firm uses two inputs in its production process: labour and capital. Using isocost and isoquant analysis, examine the possible effects of an increase in wage on the firm’s

(a) use of labour and capital

(b) long-run total and average costs.

- Problem Question:

a) Derive the cost minimizing input demands and the long-run total cost function for the following production functions assuming input prices w1 and w2:

(i) y = f(x1, x2) = 2x1 + x2

(ii) y = min(x1, 3x2)

b) For each of the production functions above, determine the short-run input demands and short run total cost function when input 2 is limited to x2 = 100 units

Explanation / Answer

ESSAY QUESTION: SOLUTION

An isoquant is presented by production function: Q = f(L, K) where L: labor & K: Capital

For analysis, we assume: f'(L) > 0, f'(K) > 0, or

MPL > 0, MPK > 0

An isocost is represented as

Total cost, TC = wL + rK where w, r: Cost of labor (wage) and cost of capital (rental rate)

Now, wage rate (w) rises.

(a) As wage rate rises, labor becomes relatively more expensive than capital. As a result, the firm substitutes more capital for labor, and quantity of labor used falls. Also, higher labor cost results in higher real cost, resulting in lower usage of labor (the now costlier input).

However, this depends on the degree of substitutability between labor and capital. If capital cannot be replaced for labor beyond a specific magnitude, amount of capital used after wage rate increase may remain unchanged at previous level. Similarly, if labor is an essential input that has a fixed proportion of usage with production function, the firm cannot use lwoer amount of labor even if wage rate rises.

(b) TC = wL + rK

As w increases, TC increases, ceteris paribus. But if K is perfectly substituted for L, then the rise is (wr) will be offset. Assuming that is not so (and the firm requires both inputs to produce), higher wage rate will increase (wL) and increase TC.

Average cost = TC / Q = (wL + rK) / Q

Since production level is assumed unchanged even after increase in wage rate, average cost rises as TC rises.

NOTE: First question is answered.

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