6. (15 points)(Monopoly) Suppose there is a market with the demand function D(p) = 1000 p. Only one firm serves this market with the cost function of (y) = y?. (a) Does this firm's technology exhibit CRS, IRS, or DRS? Explain. El ) Write down the inverse market demand function and the marginal revenue function. ) Find the optimal amount of production y*, and the corresponding market price p*. Draw the demand curve, marginal revenue curve, and marginal cost curves on a graph (put p on the vertical axis and y on the horizontal axis). (e) Find the socially optimal level of production (y**) and price (p**). El (f) Suppose the government intervenes in the market, and taxes (or subsidizes) the monopoly to bring the production level to the socially optimal level. What is the appropriate value of a quantity tax (or quantity subsidy) on y? SNote: put p on the vertical axis and y on the horizontal axis. "Hint: The cost function implicitly deliver some information on technology (the production function). You can assume that the input costs (w,wsz) are fixed at some levels. 8Hint: Find the point where the dead-weight loss is 0 (the market demand curve meets the me curve). In other words, we think of a hypothetical equilibrium point if the monopoly behaves like a competitive firm