4. Suppose you have 51250 acres of land to allocate to corn and soybeans. The production function for com is Y; = 22,',

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4 Suppose You Have 51250 Acres Of Land To Allocate To Corn And Soybeans The Production Function For Com Is Y 22 1 (30.46 KiB) Viewed 38 times

4. Suppose you have 51250 acres of land to allocate to corn and soybeans. The production function for com is Y; = 22,', where Y, is the amount of bushels of corn and Xi is the amount of land used for corn. You also know that the production function for soybeans is Yg = 1805, where Yz is the amount of bushels of soybeans and X2 is the amount of land used for soybeans. Assume that the price of corn is 30 and the price of soybeans is 10. Also assume the input cost is 9. (45 Points) A Set-up the maximization problem. B. Set-up the Lagrangean and give the first order conditions C. Please find the production possibility frontier (PPF) using soybeans as the dependent variable and corn as the independent variable? D. What is the marginal rate of product transformation (MRPT) for the PPF? E. What is the optimal output given the price ratio? F. Solve for the optimal input use by using the MVP's. G. How much revenue and profit are being brought in at the optimal outputs and input allocation? H. Please sketch the solution on a graph (Note, all the numbers on the graph may not come out to be integer numbers) 1. What is the MRPT at Y4 = 250? Please explain what this means in an economic sense