(a) Does this production function exhibit constant, increasing or decreasing returns to scale? Explain how you would be able to see this on an isoquant graph. (b) Set out the unconstrained profit maximisation problem (assuming input prices are w for labour and r for capital and the output price is p) and then solve for the unconditional input demand functions for capital and labour and find the firm's supply function. (c) Now set up the cost minimisation problem and solve for the conditional labour and capital demands. What is the difference between the unconditional input demand functions from part (b) and the conditional input demand functions you have just derived? (d) Give an expression for the total cost function (no need to simplify) and explain how the average and marginal cost functions are related to total cost. (You do not need to derive a function for AC or MC). How would you derive the supply function from this point and how would you expect it to be related to your answer from part (c)? (e) If we were to consider the short run problem for a firm, rather than the long run problem, would we expect to see their total costs being higher in the short run or in the long run? Explain your answer using a diagram to help you.

Solve all the parts and add explanation and check answer twice

In this problem annual income for ages 20 to 80 is given graphically. People sometimes spend less than their income (to save for retirement) or more than their income (taking out a loan). The process of spreading out spending over a lifetime is called consumption smoothing. annual income ($10nns nar vaar) years) (a) Find the average annual income for these years. The average annual income is dollars/year. eTextbook and Media (b) Assuming that people spend at a constant rate equal to their average income, when are they spending less than they earn, and when are they spending more? Enter your answers in increasing order. They spend less than their income every year from age to They spend more than their income every year from age to and from age to