(This problem aims at expenditure proportions and is designed to get you to use the RTS...

(This problem aims at expenditure proportions and is designed to get you to use the RTS = w/r condition in combination with different facts than you normally have, and to get you thinking about how solutions change when conditions change.)

You are processing tax returns for clients using permanent P and temporary T workers as your inputs according to the Cobb-Douglas production function q(P,T) = 3P^0.6T^0.4. You pay your permanent workers w per unit and your temporary workers r per unit. Show your work at each step of this problem.

(a) If you are in equilibrium and you have twice as many temporary workers as permanent workers, what is the ratio of per unit pay (w to r) for the two groups?

(b) What proportion of your total payroll M goes to each group? (Hint: the proportions are represented by wP and rT, each divided by M.)

(c) If temporary workers receive an exogenous (that is, from outside this model) increase in pay of 50%, and you continue to pay your permanent workers the old amount, what will be the new ratio of employment T/P?

Expert Solution

Rahul Sunny answered 2 years ago

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