1. Answer the following using the production function F(L, K) = L1/2K1/2, input prices fixed at...

1. Answer the following using the production function F(L, K) = L^1/2K^1/2, input prices fixed at w =4 and v = 9. There are two different types of firms. Big firms have SR capital fixed at 144, and small firms have SR fixed capital of 64.

a) Show that for the big firms with K = 144, SC_b(q) = q² /36 + 1296 and for the small firms with fixed capital of 64, SC_s(q) = q²/16 + 576. Use this to find SMC_b(q) and SMC_s(q)

b) Show that if the market demand is Q_D=-1900P + 41040, there is a LR competitive equilibrium with 40 big firms with a fixed capital of 144 and 100 small firms with a fixed capital of 64.

c) What does the fact that firms of different sizes can co-exist in LR equilibrium tell us about the production function? Can you verify that conclusion from the production function?

d) Show that the LR number of identical firms large firms (K=144) is 84 and this makes the LR price a little bigger than the price in (b).. Explain why “Reality” prevented us from getting the same price as in (b).

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

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