A price-taking firm produces wheels (y), using capital (K) and labor (L). The price of each Capital is 2 and Labour is 1. Price of output is denoted P.

The Cobb Douglas production function is given by, f(L, K) = L^1/6 K^1/3.

a) Calculate the MRTS

(b) Solve for the firm's long-run factor demands, L*(p) and K*(p), and the long-run supply function, y*(p).

c) There are 10 identical price-taking firms, each produces wheels with the same production function as above. r = 2 and w = 1. Define the market supply function as