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Consider the following utility function of 2 goods, x and y: U[x,y]|= [{x 101'2 + {yli'i ]; x,yal] The prices of good x and y is 10 and 20 respectively. The income is denoted by m. a] Draw the indifference curves for the utility function and use arrows to explain in which direction utility increases or decreases. [3 points] b} Find the consumption bundle or bundles that maximizes utility for the consumer. [4 poirrts] c] Find the Engel curve for both goods. [4 points] Suppose the utility function changes and now it is: mosh-101*: + {yrlure ; was: dj Draw the indifference curves for the utility function and use arrows to explain in which direction utility increases or decreases. [3 points] e] Find the consumption bundle or bundles that maximizes utility for the consumer. [4 points] f} Find the Engel curve for both goods. [4 points] Suppose that the total market demand for crude oil is given by QD = 70,000 - 2,000 P where QD is the quantity of oil in thousands of barrels per year and P is the dollar price per barrel. Suppose also that there are 1,000 identical small producers of crude oil, each with marginal costs given by MC = q + 5 where q is the output of the typical firm. a. Assuming that each small oil producer acts as a price taker, calculate the typical firm's supply curve (q = ...), the market supply curve (QS= .), and the market equilibrium price and quantity (where QD = QS). b. Suppose a practically infinite source of crude oil is discovered in New Jersey by a would-be price leader and that this oil can be produced at a constant average and marginal cost of AC = MC = $15 per barrel. Assume also that the supply behavior of the competitive fringe described in part a is unchanged by this discovery. Calculate the demand curve facing the price leader. C. Assuming that the price leader's marginal revenue curve is given by MR = 25 -V-^-r, 1,500 how much should the price leader produce in order to maximize profits? What price and quantity will now prevail in the market?Part III - Worked Problem (40 points) Assume that the market demand for oil in a country can be described by: Q =80 - 2P Also assume that oil production is controlled by the government and the cost of production can be described by: MC = 10 +Q a) What would oil price and quantity be in the country if competitive prices are charged to consumers? What is the net welfare to society at this price and quantity? b) Suppose the oil market develops into a monopoly in that country. What is the new price and quantity in the monopoly market? What is the net welfare to society at the monopoly price and quantity? c) Now, the country is allowing international trade and some competitive international producers (i.e. competitive fringe) enter the market. The marginal cost of the competitive fringe is: MC = 20 + Qc The domestic oil producer now has to face some competition, but remains a dominant firm. Applying the dominant firm model to the situation with a new competitive fringe, what would be the domestic oil producer's level of output, the price charged by the domestic producer, and what would be the competitive international producers' level of output as a group? Why is the domestic producer the dominant firm?4. (5 points) Consider the utility function u(x, y) = 10 In(x) + y. (a) Let px = 10 denote the price of x, let py = 1 denote the price of y and let / = 100 denote the income. Find the utility maximizing bundle. (b) If px = 5 and the price of y and income are as in part (a), then find the expenditure minimizing bundle to get to the utility level from part (a). (c) Fix the income at / = 100 and p. = 2. Is there any price range for y where only good x will be purchased, that is, the optimal bundle will have y = 0