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Problem 11 Suppose that for a theme park, the current marginal product of a ticket taker...

Problem 11 Suppose that for a theme park, the current marginal product of a ticket taker is 20 tickets per day, and that the current marginal product of an advertisement is 50 tickets per day. The wage of a ticket taker is $80 per day, and the daily cost of an advertisement is $200.

  1. (i) (3 points) To minimize costs, should the theme park increase, decrease or not change the number of ticket takers it employs? Should it increase, decrease, or not change the number of advertisements it is currently running?

  2. (ii) (2 points) Interpret the marginal rate of technical substitution that the theme park faces.

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Answer #1

(a)

Cost is minimized when [MP(ticket taker) / Wage rate] = [MP(advertising) / cost]

MP(ticket taker) / Wage rate = 20/80 = 0.25

MP(advertising) / cost = 50/200 = 0.25

Since [MP(ticket taker) / Wage rate] = [MP(advertising) / cost], cost is being minimized. It will not change number of ticket takers.

(b)

MRTS = - MP(ticket taker) / MP(advertising) = - 20/50 = - 0.4

It means that in order to use 1 more ticket taker, 0.4 units of advertising has to be given up.

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