101A_midterm2

# 101A_midterm2 - Econ 101A Midterm 2 Th 8 April 2009 You...

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Econ 101A — Midterm 2 Th 8 April 2009. You have approximately 1 hour and 20 minutes to answer the questions in the midterm. I will collect the exams at 11.00 sharp. Show your work, and good luck! Problem 1. Production (38 points) . Consider a farmer that produces corn using labor. The labor cost in dollar to produce y bushels of corn is c ( y )= Cy 2 , with C> 0 . There are 100 identical farms which all behave competitively. Corn sells at a price p per bushel. 1. Derive the marginal cost c 0 ( y ) and the average cost c ( y ) /y. Plot them. Derive graphically the supply curve. (Have the quantity y on the horizontal axis). (5 points) 2. Write the expression for the supply of corn y ( p ) for each f rm, and derive the expression for the aggregate supply function Y S ( p ) (5 points) 3. From now on, suppose that the demand curve of corn is D ( p ) = 200 50 p and assume C =1 . Derive the equilibrium price p and total quantity sold Y S . (5 points) 4. Derive the pro f ts of each f rm. (5 points) 5. Now assume that land is not free, and that the farmers are renting the land from a monopolist (that is, there is only one land owner, and it is impossible to rent land somewhere else). How much will the land-owner charge each of the farms? Explain. (8 points) 6. Taking the rent of the land into account, how much are the pro f ts of each f rm? (4 points) 7. In what sense there is a parallel between the presence of rents in the land and the entry of f rms in the long-run equilibrium? (6 points) Solution of Problem 1. 1. c 0 ( y )=2 and c ( y ) /y = . Since marginal cost is always larger than average cost, the supply curve is the marginal cost curve. See graph in appendix. 2. The condition p = c 0 ( y ) implies p =2 or y ( p p 2 C The aggregate supply function, summing across all f rms, is y ( p 100 X j =1 p 2 C = 50 p C 3. The equilibrium is y ( p )=5 0 p = D ( p )=200 50 p p (50 + 50) = 200 p and Y S = 100 y ( p ) = 200 50 p = 100 1

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4. Since Y S =100 ,each f rm produces 1 unit and earns pro f t π = p y c ( y )=2 1 2 =1 5. Since land does not enter the corn production function, the land rental price ( r )i sa f xed cost the farmer must pay to operate. Fixed costs do not change the farmer’s pro f t-maximizing choice of y , but if pro f tisnegat iveatthat y , the farmer will choose not to produce at all (exit the industry). In this case, given the pro f ts calculated above, no farmer will pay more than \$1 for land. Every farmer will pay any price less than or equal to \$1, however, because operating will still be pro f table. So the monopolist faces a land demand curve that is perfectly inelastic for r 1 : D ( r )= ( 100 if r 1 , 0 if r> 1 . Given this demand, the monopolist maximizes his own pro f ts by setting r : the monopolist extracts all the farmers’ pro f tasrent .
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101A_midterm2 - Econ 101A Midterm 2 Th 8 April 2009 You...

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