Midterm 2(ans).pdf - Name Intermediate Microeconomics Inst...

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Name__________________________________ Intermediate Microeconomics Inst. Mario B. Muzzi Midterm 2 (Model Ans) 1) (6pts) Short Run Cost Curves: The curves below reflect information about the cost structure of a firm. Use the figure to answer the following questions: a. (2pts) Identify by letter which of the curves above is average total cost _B__, av- erage fixed cost __D__, average variable cost __C__, and marginal cost__A__. b. (2pt) Describe the relationship between curves B and curve C. B is the ATC and C is the AVC. They are separated by AFC. As the quantity of output increases the ATC and AVC get closer because the AFC is falling. They will never intersect. c. (2pt) Describe the relationship between curves A and B. A is the MC and B is the ATC. A drives B. A pulls B down when A is below B and pulls B up when A is above B. A intersects B at B’s lowest point. This is where B’s slope is equal to zero. 2) (15pts) Long-Run Production and Profit Maximization Dominic’s Manure Co. is a pro- ducer of fertilizer. There are two inputs that make the manure fertilizer: Cows (C) and Hay (H). Cows cost $4/pound and Hay costs $2/pound. The production function for Dominic’s
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Manure Co. is given by q = 24C – 0.5C 2 + 18H – 0.5H 2 . Currently the company has an ex- penditure constraint (budget) equal to $52. a) (7pts) Derive the profit-maximizing level of Cows (C*) and Hay (H*) for Dominic’s Manure Co. subject to their budget constraint. Z= 24C-0.5C 2 + 18H-0.5H 2 + λ (52-4C-2H) dZ/dC = 24-C-4 λ =0 dZ/dH = 18-H-2 λ =0 dZ/d λ = 52-4C-2H=0 24-C-4 λ =0 -2(18-H-2 λ =0) 24-C-4 λ =0 -36+2H-4 λ =0) C=2H-12 52-4(2H-12)-2H=0 100=10H H=10 52-4C-2(10)=0 32=4C C=8 b) (3pts) Show that the “profit maximizing rule” (a.k.a. the MRTS is equal to the input price ra- tio) at C* and H*. MP C /MP H = P C /P H (24-8)/(18-10) =$4/$2 2/1 = 2/1 c) (2pts) Find q* with the optimum level of inputs. q = 24C – 0.5C 2 + 18H – 0.5H 2 q = 24(8) – 0.5(8) 2 + 18(10) – 0.5(10) 2 q = 290 d) (3pts) Suppose the market price for manure is $10/sack. How much is profit at q*? π =TR-TC $2,900-$52 $2,848 3) (9pts) Production and Costs: Briefly describe the following terms by explaining when, how or why they may occur. a) (3pts) The law of diminishing returns:
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This occurs when an increase in labor results in less of a gain in output than the previ- ous increase in labor. This occurs in the short-run when capital is fix which con- strains the gains from an increase in labor. b) (3pts) Diseconomies of scale: This occurs when inputs are increased by a certain percentage, while output increases by a lower percentage. As a result, the average cost of production increases as the firm increase its output. This occurs in the long-run when all factors of production can be changed. c) (3pts) Constant Cost Industry: This occurs when new firms enter an industry. As the market output increases, it causes an increase in demand for inputs. However, the increased demand does not cause the price of inputs to rise.
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  • Fall '10
  • AUFFHAMMER
  • Economics, average total cost

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