managerial economics class

1, In the type of economic forecasting known as barometric forecasting, the notion of a diffusion index has been developed to help us better use leading economic indicators for forecasting purposes. What, specifically, is measured by the diffusion index? Also, what, specifically, would a diffusion index of 40 imply or suggest about which phase of the business cycle the economy is in?

2, Your unfortunate friend, who has not taken a course in economics, tells your that the law of diminishing returns is incorrect. He bases this conclusion on the fact that a small brewery in his hometown now has six plants throughout the country and is producing more beer than ever. Explain why his conclusion is incorrect, beginning with a formal statement of the "law of diminishing marginal physical returns."

3, Suppose there are two factors of production (inputs) named "L" and "K" which a business firm uses to produce a particular product. Using a graph in the input plane, graphically illustrate and explain in words the condition for minimizing the total cost of producing a given level of output or for maximizing output subject to a given total cost (expenditure). Include in your answer the mathematical relation which holds when this condition of "producer efficiency equilibrium" is reached.(The use of an isoquant(s) and an isocost curve(s) is appropriate here. Carefully label everything in your graph and be as neat as possible. Be thorough.)

4, Is the use of a least cost combination of inputs necessary for long-run profit Is it sufficient to ensure that profit is maximized? Why or why not?