3. Big Boy Corp. is the largest producer of numos. It has acquired this position

Question

3. Big Boy Corp. is the largest producer of numos. It has acquired this position because it has a patented process which allows it to produce numos according to the cost function: CQ,) 10+ (Q/100) Each of the other firms in the industry (there are 100 other firms) uses an older process, characterized by the cost function c(q) = q2+5q + 10. Demand for numos is Q1 = 1000-50p. Assuming that Big Boy acts as a price leader, what will be the price of numos, the total quantity produced, and the quantity produced by each firm in the short run? (a) (b) If, in the long run, entry can take place freely by firms using the old technology, what will be the price and total quantity of numos, and also the output of each firmi?

Explanation / Answer

Answer : [Q= K^{1/2}L^{1/2}]

[MP_{L}= K^{1/2}1/2L^{1/2}]

[MP_{K}= L^{1/2}1/2K^{1/2}]

[MRTS=K^{1/2}/2L^{1/2} /L^{1/2}1/2K^{1/2}]

[MRTS=K/L]

This shows that equal amount of capital and labor should be used to produce 100 units of output.

It means that in place of K we use L

100 = k1/2L1/2

100= K

Therefore 100 units of K and L is used to produce 100 units of output.

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