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economics 101A mid term(matter unclear, check the attachment)

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Question;Econ 101A;? Midterm 2;Th 10;April 2014.;You have;approximately 1 hour and 20 minutes to answer the questions in the midterm. We;will collect;the exams;at 11.00 sharp. Show your work, and good luck!;Problem;1. Monopoly with Fixed Cost.(55 points + extra credit).;Consider the case of a;monopolist;producing quantity?with total cost?(?) =?+???with??0and??0?;1. Comment;briefly on the cost function. Does it involve a fixed cost? (5 points);2.;Determine the marginal cost function?0?and the average;cost function?(?)???and plot the two;functions;in a graph with x-axis quantity?and y-axis cost/price. (5 points);3. Assume;now that aggregate demand is given by the linear (inverse) demand function?(?) =?????;with????Draw it in the;graph with the marginal cost function of point (2). If you want, assume;?= 10??;= 5??= 1??= 1(just for the graph) Also, derive the marginal revenue??function, by;differentiating;with respect to?the revenue??and draw the??=?0function in the graph. (5;points);4. Find;graphically the solution for monopoly quantity and price (5 points);5. Still;graphically, indicate the producer surplus or profits of the monopolist.;Indicate which of the two;methods you;are using. (5 points);6. Now;solve analytically for the monopoly solution, by maximizing;max;?;???(?)??(?) =?(????)??????;Obtain the;first order conditions and solve for??and???the monopoly;solution. (5 points);7. Compute;now the profits analytically, plugging in??and??in the solution above. (5 points);8. A;consultant to the government claims, regarding this monopoly: ?A big problem;with monopoly in;this;industry is that profits are unfairly high?. Is that always true? Can you give;conditions under;which;monopoly profits in this case would bezero? (10 points);9.;Continuing on the point above, can you give conditions under which monopoly;would havenegative;profits?;Going back to the figure, what would the average cost curve look like in that;case? What;would the;monopolist do in that case? (5 points);10. Given;the above point (9), revise the solution at point (6) for the optimal monopoly;solution. (5 points);11. (Extra;credit, do not attempt till you have done Problem 2) If we were in perfect;competition, and;each firm;had the same cost curve as above, and faced the same demand curve is as above;what would;be the;supply function and what would be the perfect competition equilibrium, if any?;Why? (15;points);1;Problem;2. Search for the Unemployed.(45 points);We consider;the problem of Ivan, an unemployed worker looking for a job in period?(sorry Ivan!). Ivan;has utility;over consumption?(?)?with?concave, that?0(?)?0and?00(?)?0for all??0?As long as;Ivan is;unemployed, he consumes the unemployment benefits??that is?=??If he can get a;job, he consumes;instead the;wage????and thus?=??Assume that?(for search effort) is the;probability that Ivan will;get a job;in period?+ 1. Thus, with probability?Ivan earns?at?+ 1?while with probability1???;Ivan;earns?.;1. Assume;first that the probability?is given, and write down the expected utility of consumption of;Ivan in;period?+ 1. (5 points);2. Now we;assume that Ivan chooses the probability?of finding a job optimally. Namely, Ivan?s utility;in period?is given by the cost of effort;of searching for a job??(?)?with?0(0) = 0??0(?)?0and;?00(?)?0for all??[0?1]?That is, search is costly, and;increasingly so at the margin. The utility in;period?+ 1is as in point (1). Write the intertemporal utility as of period??that is, the sum;of the;period-t;utility (the cost of search) and the discounted period-t+1 utility (the;consumption). Assume;that the;utility at period t+1 is discounted by the discount rate??(5 points);3. Maximize;the expected utility with respect to?and derive the first-order conditions. Interpret the first;order;conditions in terms of marginal cost of effort??and marginal benefit of effort??Do not worry;about the;corner solutions (that is, the constraint that0???1) (5 points);4. Write;down the second order conditions. Are they satisfied in light of the properties;of?(?)? (5 points);5. An;advisor to the president would like to know how the intensity of search by the;unemployed would;be affected;by an increase in unemployment benefits. Using the first order condition and;the implicit;function;theorem, obtain the expression for???????What sign does it;have, and what is the intuition?;(5 points);6.;Similarly using the first order condition and the implicit function theorem;obtain the expression for;???????What sign does it have, and what is the intuition? (5 points);7. The;advisor also is studying a subpopulation that is very impatient, that is, has;high discounting??;and would;like to know how that affects optimal search. Similarly using the first order;condition and;the;implicit function theorem, obtain the expression for???????What sign does it;have, and what is;the;intuition? (5 points);8. The same;advisor now would like to know whether the unemployed would be made happier by;higher;unemployment;benefits. Use the envelope theorem to show how the utility at the optimum would;be;affected by;an increase in benefits. What sign does it have, and what is the intuition? (10;points);2

 

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