Consider a firm with the production function. Y =KL

1. Show that the firm has increasing returns scale. That is: output increases more than proportionally when both inputs are doubled.
2. Formally, the cost functionisC(Y)=2*sqrt(y). What is average cost?(sqrt =square root or y to the 1/2)
3. Explain, by referencing average costs, why such a firm is a natural monopoly.
4. Verbally explain the marginal revenue for such a firm. Why is marginal revenue not simply the market price as in the purely competitive case? You can assume that average revenue (the demand curve) is linear.
5. You are a public-spirited regulator (not susceptible to bribes). Your objective is to insure that every consumer who values the good at or above its marginal cost is able to make a purchase. Assume there is one uniform price in the market. Diagram the average and marginal revenue curves and the average and marginal costs. (You don't have to be extremely precise with values in your graph). Why is the firm unhappy with your policy objective?
6. In this setting, we suppose the firm knows the demand curve: that is the firm knows the reservation value or maximum WTP of each consumer (perhaps they have an economist on staff familiar with incentive compatible elicitation mechanisms). The firm argues that if you allow them to charge different prices to different people they will be happy and you will meet your policy objective. Explain the logic of their strategy. Use a diagram if it helps you explain.