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Exercise: Factor Market

1. If a firm has the following production function,


and the firm is a monopoly with the following demand curve,


find the MRPL equation for this firm.

  • Step one, solve for the MPL:

  • Step two, find the revenue function and derive the MR:

  • Step three, remember the formula for the MRPL:


2. the demand and supply for labor in a market are as follows:


  • Find the equilibrium wage rate and quantity of labor hired:

  • Find the economic rent for workers at the equilibrium wage rate:

  • If the workers want to optimize their economic rent, is the wage from part a the one they would choose?
No, the economic rent is optimized by looking at the intersection of the MR and supply curve.


You can see that if I set my wage at about $7.78, the economic rent for the workers is much bigger than the one found at the equilibrium wage rate.

Source: the problems were inspired by the exercises on pages 297-298 in Study Guide For Microeconomics, 8th edition (2013) by J.Hamilton, and V.Suslow.

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Location: New York, NY, USA

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