Section 7 Notes

# Section 7 Notes - Q15 Chap 5 of Binmore A firm makes...

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Q15, Chap 5 of Binmore A firm makes sprockets that sell at \$8 each. To make sprockets, it requires various inputs, but these are all free except labor. The number of sprockets produced in a day, s = l , where l hours of labor are used. If the hourly wage is w , explain why the firm’s daily profit is π = 8 l - wl . If the worker regards each hour of leisure as being worth \$1, explain why his daily income is I = wl + (24 - l ). Both the worker and the firm are risk neutral.

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1. Find the value of l that maximizes the sur- plus π + I available to the firm and worker jointly.
The total surplus is, π + I = 8 l + 24 - l . Setting its derivative w.r.t l to 0. 4 l - 1 / 2 - 1 = 0 l = 16 . Note that at l = 16, the maximum surplus of 40 is attained.

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2. Suppose the worker and the firm bargain about both the wage and the number of hours to be worked. What is their dis- agreement point? How will the surplus be divided if the regular Nash bargaining so- lution is used? What wage will be agreed upon? What will be the length of the work- ing day?
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• Fall '06
• TODD,M.
• Bargaining, Firm, Nash, Nash bargaining game, disagreement point

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