Exercise 3: The Producer's Cost Minimization Problem Consider a rm that uses two inputs to produce one output. The rm's production technology can be described by the production function y = f(21122) = 2Z1 +3\\/;2 4. Use your previous answer to find the firm's (long-run) cost function C(y) = w1 . z1(y) + w2 . zz (y) at the given input prices. 5. The firm's (long-run) expansion path is defined as the set of all input bundles that are optimal at the given prices for some output level y 2 0, i.e. it is the set {(21, z2) E R4 (3y > 0 such that z1 = z1(y; W1, W2), Z2 = zz(y; W1, W2)} . For input prices w1 = 1 and w2 = 3 find the firm's long-run expansion path