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## Microeconomics Question from Walter E. Williams:

You are the absolute czar and head of a union of 1,000 plumbers in Austin, Texas. You have the absolute power to set the wage at which the plumbers will work. The economist that you have hired tells you that the demand for plumbers in Austin is Q = 1,200 - 100W, where Q is the number of plumbers employed and W is their wage. If there were no other plumbers in Austin, what wage would you set if

• (a) you wished to achieve full employment at the highest possible wage,
• (b) you wished to achieve maximum total payments to plumbers? Get the elasticities of demand for plumbers at the wages identified in (a and b) both answers.

## Answer

A) in order to achieve full employment and the highest possible wage, we would need to set the wage at the point where the marginal product of labor was zero. At this point, the highest level of employment would be realized at the highest wage for full employment. B) If we are only interested in maximum payments to plumbers, we would set the wage at the point were the marginal product of labor was at its maximum. This would ensure the highest wage and would be at a level of employment that was less than full employment.

• To find answer to a: Your quantity is 1000 plumbers, and the demand function is Q=1200 – 100W. You plug in the quantity of 1000: 1000 = 1200 -100W, and solve for W. Answer: \$2.
• To find answer to b: Start with total cost …which is price x quantity. Since Q = 1200 – 100W, multiply by W to get TC. TC = 1200W – 100W2. Then take the derivative to find the marginal cost: MC = 1200-200W. Set MC = 0, and solve for W: 1200 -200W =0  W=6. If W is 6, then 600 plumbers will be employed.
• To find the elasticity for a: ∂Q/∂P*P/Q. In this case, P is the wage of \$2, and the Q is 1000. The ∂Q/∂P from the demand function is -100. Therefore, -100*(2/1000) = -0.2. This is inelastic.
• To find the elasticity of b, it is the same ∂Q/∂P of -100, but use P=\$6 and Q=600. Therefore, -100*(6/600) = -1 This is unit elastic.

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