Hi, I'm after some assistance with some microeconomics questions, any help is much appreciated.

1. Consider the Cobb-Douglas production function y - AK"L , where y is output, K is the quantity of capital, L is the quantity of labour, and A, a, and P are positive constants. What values of a and/or P satisfy the following conditions? a. Decreasing marginal product of capital b. Increasing marginal product of labour c. Decreasing returns to scale d. Increasing returns to scale e. Constant returns to scale 2. Consider a firm whose production function is /(K, L) = 1000 min (3K, [) . a. Sketch isoquants for q = 3000 and q = 6000. b. If capital is fixed in the short run at K - 5, sketch the total product curve as L rises. c. Refer to (b) and sketch the marginal product of labour curve. 3. If we plot the profit of a small business against the number of leave days (days away from work) the owner takes, we find that profit first rises with the number of leave days (a few days off improves the owner's effectiveness as a manager the rest of the year), but eventually falls as she takes more leave days. a. Draw a graph showing the relationship between leave days (on the horizontal axis) and the firm's profit (on the vertical axis). This is the owner's budget constraint. b. Suppose the owner's preferences over bundles of profit and leave days are represented by indifference curves with the usual shape (downward sloping, convex, etc.). Add one or more indifference curves to your graph from (a), so that the owner's optimal bundle can be seen. c. Will the owner take the number of leave days that maximises the firm's profit? If so, explain why. If not, explain what the owner actually will do, and why. 4. Suppose that production of a product requires two inputs. If the prices of the inputs are equal, then is the correct optimal allocation to employ these inputs in equal amounts? Explain why or why not