Homework Answers
Note that at the optimum production mix MPL/w = MPK/r
Here for type A firms, we have 1/8 < 2/10 which means these firms will use only capital. Then we have x = 2k or k = 0.5x. Cost function is C = r*K or C = 10*0.5x which becomes C= 5x. Marginal cost is $5.
Here for type B firms, we have 2/8 > 1/10 which means these firms will use only labor. Then we have x = 2l or l = 0.5x. Cost function is C = w*L or C = 8*0.5x which becomes C= 4x. Marginal cost is $4.
In the long run only type B firms will survive due to lower marginal cost. Then we know that each firm will hire 1 labor unit, produce x = 2*1 = 2 units and pay 1*8 = $8. Since MC is $4, long run price is $4 and the quantity is 200 – 2*4 = 192 units.
Number of firms = 192/2 = 96
The answer is 96
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