专业课资料 练习题 真题 中心习题 2007-fll-micro

1 Intermediate Microeconomics Homework 1 Due in class on Sept 27th 1 Use the following equations to answer the questions below 11005 d QP and 100 s QP a Find the equilibrium price and quantity b Assume that sellers are granted a 20 per unit subsidy What is the new price paid by consumers for this good What is the new total price total price means price inclusive of subsidy received by sellers What is the new equilibrium quantity c Assume instead that the 20 per unit subsidy is granted to buyers Answer the same question in part b d Calculate s eand d eat the original price and quantity Using these elasticity values verify your answer to part b and c by using the following ssd d dPeeedSubsidy 2 Suppose that the only way to reach a certain restaurant is by train and the train fare is 3 One day a law is passed requiring the restaurant owner to provide free transportation to his restaurant which he does by making an arrangement with the railroad whereby his customers ride free and he pays the 3 fare per customer directly to the railroad a What does this do to the supply curve for restaurant meals b What does this do to the demand curve for restaurant meals c Compare the following the price customers paid for meals including transportation costs before the law vs the price customers pay for meals after the law is passed Make a similar comparison for the seller d Does anybody benefit by this law 3 Find the x MU y MU and MRS equations for each of the following utility function and indicate which of them exhibit diminishing MRS that is which of them yield convex indifferent curves a 0 60 4 Uxy b 22 Uxy x y 0 c 24Uxy d 22 Ux y e ab Ux y a b 0 4 Assume Ux y I 100 10 x P and 5 y P Use the Lagrangian method to 2 find the optimal values of x and y 5 For each case below draw a graph of the budget line Indicate the values of X and M at the kinks and intercepts Assume I 100 1 x P Note that M represents all other goods than x and its price is assumed to be 1 unit a The government provides a per unit subsidy of 0 50 X so the consumer faces a price of 0 5 unit but only beyond the first 10 units of X b The government provides a per unit subsidy of 0 50 X so the consumer faces a price of 0 5 unit but only up to the first 10 units of X c The government introduces a program in which the first 5 units of X are free After that the government provides a per unit subsidy of 0 50 X so the price of X to consumers is 0 50 unit but only up to 10th unit of X the government does not provide any subsidy for units purchased beyond the 10th unit The consumer still retains the gift for the earlier units d Same as in part c except that in this case if the consumer consumes more than 10 units of X the government takes away ALL subsidies i e the consumer no longer gets the first 5 units for free etc Intermediate Microeconomics Homework 2 Due in class on Oct 18 1 Assume the following P 0 10 9 UFM X 1 and I 100 a Find the optimal consumption bundle and the level of utility at that bundle Show the result from this part on a graph b Suppose the government now grants the consumer 20 worth of food stamps Find the new optimal consumption bundle HINT To find the solution proceed as follows i Assume that the consumer had instead been granted 20 cash and find the optimal bundle under this assumption ii Now see if that bundle is actually obtainable under the food stamp program does it lie on the food stamp budget line or above it If it is NOT obtainable then that cannot be our solution Rather the solution would be the bundle that is nearest to this bundle c What is the MRS at the bundle selected in part b d Suppose the consumer can sell his food stamps for 70 of face value hence the effective price of food for F 20 is 0 70 Draw in the budget line corresponding to this new situation Use the same graph as used above Now draw in the IC the consumer was on in part b BE CAREFUL how you draw it you will find the information about the MRS from part c and the slope of the budget line under this new situation useful in drawing in this IC e Based on your graph will this consumer end up selling some of his food stamps Explain f Find the optimal consumption bundle when the consumer can sell his food stamps for 70 of face value HINT To find the solution assume that the consumer has additional income of 14 the dollar value received if the consumer sold off all of his food stamps 0 7 20 14 How many food stamps are sold Draw the IC corresponding to this outcome on your above graph 2 Suppose that the only two goods consumed are food and housing Assume that housing is an inferior good Now the price of food rises a Illustrate the substitution and income effects How does your graph reflect the fact that housing is an inferior good b True or false When the price of food increases you certainly consume more housing than before Explain 3 A firm faces the following production function Q 4L0 5K0 5 a Find the MRTS b Given PL 4 and PK 4 find the most efficient combination of L and K required to produce 16 unites of output c What is the TC of producing 16 units of output d Suppose the government subsidizes the cost of capital such that the price paid by the firm is now PK 2 Holding Q fixed at 16 units what is the cost minimizing combination of L and K to the firm What is the total cost for the firm How much does the firm save in costs What is the total cost of the subsidy to the government Is this subsidy efficient Explain e Using the data given in parts a and b derive this firm s long run total cost function f What does a graph of this long run TC function look like What are the MC and AC function Draw the MC and AC curves g If we assume that K is fixed at 4 in the short run what would the short run TC function be short run MC function short run AVC function short run AC function 4 Assume that the short run production function for a given firm is Q 2L0 5 The price of labor p is 8 labor and FC 50 a Find the VC and TC functions b Find the AC AFC AVC and MC functions Draw a graph of the AVC AC and MC curves c At what quantity does MC equal AC d Find the equation for firm s supply curve e Suppose this firm is a price taker and faces a price of 80 What is the profit maximizing output at this price What is profit at this price and quantity Is this a long run equilibrium Where will price end up in long run ignore factor price effect f Find the market supply curve assuming there are 100 identical firms in the industry g Assume that the market demand curve is QMd 2800 10P Using this information along with your answer to part f calculate the equilibrium price h Assuming a constant cost industry how many firms will there be in this industry in the long run i Show all of the above graphs 5 Suppose the government guarantees wheat farmers a minimum price of P Assume that this price lies above the price that would exist without any government intervention The government guarantees this price NOT by buying up any surplus of wheat that may exist at P but rather by making up the difference between whatever price wheat farmers get on the open market Firm 2 s Reaction Curve Q2 40 0 5Q1 Q1 Q2 26 67 P 36 66 12 711 29 c An even split of cartel output means that each firm produces 20 units recall from part a that monopoly output is 40 This is not stable since a quantity of 20 is not on either firm s reaction curve In fact given that firm 2 chooses 20 units firm 1 s best choice is Q1 40 0 5Q2 30 The same can be said of firm 2 So both firms cheat on the cartel agreement by producing more than 20 units This will lead us back to Cournot solution d Q1 40 Q2 20 P 30 1 800 2 400 joint 1 200 Show the graph by yourself 3 a Store 2 has a dominant strategy promote Product Y Store 1 does not have a dominant strategy b The pure Nash equilibrium for this game is Store 1 promote product X and Store 2 promote product Y 4 a No Nash equilibrium in pure strategies exists b Mixed Nash equilibrium Player 1 plays UP with a probability of 0 5 and DOWN with a probability of 0 5 Player 2 plays UP with a probability of 0 25 and DOWN with a probability of 0 75 Player 1 s expected payoff 25 Player 2 s expected payoff 10 5 a Both firms have a dominant strategy Low price is both firms dominant strategies The Nash equilibrium is Low price Low price b If Firm 1 was to cheat on this agreement by charging a l