Question

What is the expansion path for the firm with the production function of f(L, K) = (L+1)K

Answer 1

The production function is given as . The different equilibrium points of cost minimization, or profit maximization, of different quantities and isocost lines corresponds to the expansion path for the firm.

Suppose price of labor is w while price of capital is r, hence the cost fucntion will be as . The optmila bundle will be where the marginal rate of technical substitution (MRTS) will be equal to the slope of the isocost line. The MRTS can be found as or (as MRTS will be for a constant quantity) or or . The slope of the isocost line can be found as or or or . Hence, the optimal bundle will be at where , ie or , which is the expansion path. It can be further written as , as the equation of the expansion path.