i. Write the first-order conditions for profit maximization characterizing the optimal use of capital, labor, and land inputs by the firm. ii. What is the elasticity of the optimal choice of capital per unit of land % to the price ratio 11;? What is the elasticity of the optimal choice of labor per unit of land % to the price ratio %? iii. Given optimal input choices. does the land share 1339 vary with the land price P? If so, in which direction does it vary when P increases? iv. Demonstrate whether, given optimal input choices, the firm earns positive profits, negative profits, or zero profits. You may wish to use the following result. Proposition (Euler's Theorem): For any differentiable constant returns to scaie production function with N inputs F(X 1, ..., X N), the foiiowing relationship hoids N19}? 1:1 6X1; F(X1,...,XN) : Xi