Problem set 3 2 Cl Suppose that the cost of producing q bottles of Punk beer is C(q)=3+8. (i) If we are modelling a Microbrewery's decision of many bottles of Punk beer to produce, specify the primitives of our model: The Decision Maker, the set of alternatives A, the preferences of the DM. (ii) Find expressions for xed cost, marginal cost, average total cost and average variable cost as functions of q. Sketch them in a diagram. (iii) Suppose that the Microbrewer is a price-taker, i.e., they consider the price p as given and nd the level of q that maximizes prot pugC(61). How much would a micro-brewery supply as a function of q? Sketch the supply curve in your diagram if the Micro-brewery has to pay the xed cost of 8 even when q=0 (Short-run). Express prots as a function of 1). (iv) Suppose now that the Microbrewer is a monopolist, i.e., they consider the price p(q) to depend on how much they produce, according to the demand function. Suppose further that the demand for Punk beer as a function of the quantity in the market is given by P(q) = 1000 - 2q. So now, to maximise prots they nd the level of q that maximises prot p(q)xq-C(q). How much would a micro-brewery supply and at what price would they sell if they pay the xed cost 8 anyway (short run)? In the long run, will this Microbrewery stay in the market? (v) Suppose again that the Microbrewer is a monopolist, i.e., they consider the price p(q) to depend on how much they produce, according to the demand function. Suppose that the Microbrewer can introduce price discrimination in two different ways: (i) She can freely set a different unit price for buying one bottle and another unit price for six packs. (ii) She can sell bottles of Punk beer to students at a different price to the rest of the population. How will the prots achieved from each of these methods of price discrimination compare with the prots you have calculated in (iv) above? Without further details, can you conclude that one of these methods is better than the other