Goleta Brewing Company hires only two types of labor, managers and brewing assis

Question

Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted by M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = m5 B5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of manager’s decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition? Solve analytically.

Explanation / Answer

Q = M0.5B0.5 = 10

MPM = dQ / dM = 0.5 (B0.5 / M0.5)

MPB = dQ / dB = 0.5 (M0.5 / B0.5)

MRS = MPM / MPB = B / M

In equlibrium, MRS = PM / PB = 50 / 10 = 5

Or, (B / M) = 5

B = 5M

Putting in production function:

10 = M0.5B0.5 Or

10 = M0.5 x (5M)0.5

M = 4 (Rounded off)

So, B = 5M = 20

If wage of M = 30, price ratio = 30 / 10 = 3

So, MRS = 3, or (B / M) = 3

B = 3M

From production function,

10 = M0.5 x (3M)0.5

M = 6

B = 18

Intuitively this result is correct. As manager's wage becomes cheaper, the firm will replace costlier brewing assistants by cheaper managers.

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