I True or false（2points*10）.1.Since a monopoly charges a price higher than marginal cost, it will produce aninefficient amount of output.2. A duopoly in which two identical firms are engaged in Bertrand competition willnot distort prices from their competitive levels.3.The change in producer's surplus when the market price changes from p1to p2ishalf of the area to the left of the marginal cost curve between p1and p2.4.If the production function is f(x1;x2) = min(x1 ,x2); then the cost function isc(w1;w2;y) =min(w1;w2;y )5. A monopolist with constant marginal costs faces a demand curve with a constantelasticity of demand and does not practice price discrimination. If the government imposes a tax of $1 per unit of goods sold by the monopolist, the monopolist will increase his price by more than $1 per unit.6.John purchases two goods, x and y. Good x is an inferior good for some range ofincome, there must be another range of income for which good x is a normal good.7.Ambrose’s utility function is U(x,y)=x+4y1/2. The price of x is 1 and the price of yis 2. If his income rises from 100 to 150, his consumption of y increases by more than 10% but less than 50%.8.Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more. Billhas convex preferences. If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.9.In a competitive pure exchange economy, if the total value of excess demand forall types of food is zero, then the total value of excess demand for all nonfood commodities must be zero.10.In Nash equilibrium, each player is making an optimal choice for herself, giventhe choices of the other players.II Fill in the blanks for the following questions（2points*10）: (1)Professor Stern's colleague, Dr. Schmertz, gives one midterm exam and a Finalexam. He weights the final twice as heavily as the midterm to determine the course grade. No grades can be dropped. If the midterm score is represented on the horizontal axis and the final score on the vertical axis, and if a student in Dr.Schmertz's class cares only about her course grade, her indifference curve is a line with slope ___________.(2)Casper's utility function is y3; where x is his consumption of cocoa and y isx+his consumption of cheese. If the total cost of x units of cocoa is 2x; if the price of cheese is 10, and Casper's income is $260, how many units of cocoa will he consume?____________(3)Brand X is one of many firms in a competitive industry where each firm has aconstant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase?____________________(4)An industry has two _rms. The inverse demand function for this industryis q=. Both firms produce at a constant unit cost of $32 per unit. What is p292-the Cournot equilibrium price for this industry? _________________________ (5)One unit of zinc and one unit of copper are needed to produce a unit of brass. Theworld's supply of zinc and the world's supply of copper are owned by two different monopolists. For simplicity assume that it costs nothing to mine zinc and copper, that no other inputs are needed to produce brass and that the brass industry operates competitively. Then the price of a unit of brass equals the cost of the inputs used to make it. The demand function for brass is p=where p is900-q2 the price of brass. The zinc and copper monopolists each set a price, believing that the other monopolist will not change his price. What is the equilibrium price of brass? ___________________III. Calculation (25 points)1. For a typical Cobb-Douglas technology, use calculus to derive the cost function of the firm.(10 points)2. Smith is the owner of a sole mineral water spring in an isolated economy. It costs Smith $2 per gallon to get his water bottled. The inverse demand curve for Smith’s water is p = 20 - q / 5 , where p is the price per gallon and q is the number of gallon sold.a. Write down an expression π(q ) for profits as a function of q. Find theprofit-maximizing choice of q for Smith, and the corresponding price and profit.(10 points)b. Suppose now Henry, Smith’s neighbor, finds also a mineral spring that producesmineral water just as good as Smith’s, but it costs Henry $6 a bottle. The total market demand remains as before. Determine the Cournot duopoly equilibrium.(5 points)IV. Graphing and Analysis (35 points)1. Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences.Draw the indifference curves corresponding to Randy’s preference. (10 points)2. Derive graphically the labor supply curve from the optimal choice of a consumer who has endowment of two commodities: labor and other goods. Note that both are desirable.(10 points)3. Assume individuals are choosing between housing services (H) measured in square feet and consumption of all other goods (C) in dollars. Suppose now the government agrees to subsidize consumers by paying 50% of their housing cost.a. Draw to show how will the budget line of a typical consumer change? Showalso her original choice and the new choice. (5 points)b. Show in the same diagram the minimum amount of income supplement the government would have to give the consumer instead of the housing subsidy to make them as well off as she was in Part a. (10 points)。