Question

9. Please derive MC- w/MPP, using the production and cost relationships. (Hint: define and apply the definition of MC.) (5 points) 10. What is the short-run decision rule for producing an output? Please explain. (5 points) 11. Explain the intuition of why the optimal output occurs when marginal revenue equals marginal cost. (5 points) 12. Please explain the shutdown rule. Using the profit function, please create an example not presented in class of a situation when you would shut down and when you would produce 13. Please explain how you decide what level of inputs you use to produce an output. Show this 14. Please explain how you decide what level of outputs you produce given a fixed level of an Use a table to discuss why you would shut down or produce under each situation. (5 points) on a graph. (5 points) input. Show this on a graph. (5 points) 15. Suppose your goal this year is to produce 6,400 bushels of organic com. Suppose your production technology has the following relationship for producing bushels of corn Q- f(L,T) = LT where Q is the number of bushels of corn you produce, L is the number of labor hours you utilize, and T is the number of tractor hours you utilize. You know that the cost per hour of labor is $20 and the cost per hour of tractor time is $500. Assume that you are a cost minimizing producer. (30 points) Theoretically, tell me how you would figure out what your minimum cost is for producing a quantity of 6,400 bushels of com. How much money will you need to ask from your banker to achieve your goal? (Note: when given your particular production function, the optimal amount of input formulas are LmlePr and T= time.) a. b. Pi, where pu is the cost of labor and pr is the cost of tractor Pr c. Please sketch a graph of this solution. Include the isoquant and iso-cost line. d. Suppose after reviewing your business plan, your banker tells you she is only willing to give you $8,000. Theoretically, tell me how you would figure out what your maximum production is when you have only $8,000 to work with and you are a cost minimizer. What is the maximum amount you can produce? (Note: when given a particular expenditure E and you are trying to maximize output, the optimal amount of input formulas are L=_ and T tractor time.) e. E and TE 2p where p is the cost of labor and pr is the cost of 2p Page 2 of 3

Answer 1

9) MC refers to the cost of producing one additional unit of output which is independent of fixed cost. MPP refers to the additional output generated by one additional unit of input(such as worker).

Deriving MC= w/MPP

=> MC= change in Total variable cost(TVC) / Change in Quantity(Q)

=> $MC=\frac{\Delta TVC}{\Delta Q}$

$\frac{\Delta TVC}{\Delta Q}=\frac{w\Delta L}{\Delta Q}$..........................................(1)

TVC changes when wages(W) given to one additional worker(L) changes.

$MPP=\frac{\Delta Q}{\Delta L}$

$=>\frac{1}{ MPP}=\frac{\Delta L}{\Delta Q}$............................(2)

Using equation (2) in equation (1) we get

$\frac{\Delta TVC}{\Delta Q}=\frac{w}{MPP}$

$or$

$MC=\frac{w}{MPP}$

Hence derived.

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10) The output is produced where profit is maximized. In short-run, a firm will produce up until the point that Marginal cost equals Marginal Revenue(MC=MR). This is based on the fact that the total profit is maximized at that point. After that point profit starts to decrease and before that point profit is not at its maximum. This is the point where marginal profit equal to zero and the firm will always continue to produce unit marginal profit is zero. This condition is known as short-run production decision.

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11) When MR= MC, the profit of the firm is at its maximum. After that point when MC>MR, the profit will start to decrease because of the Marginal cost of producing an output is more than the revenue earned. And before that point when MC<MR, the firm can earn more profit by producing more of the output. So the point MC=MR is the optimal point to produce the output.

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12) The shutdown rule tells that "the firm must continue to operate if price exceeds the average variable cost(P>AVC) otherwise the firm must shut down(P<AVC) immediately".

Profit function(P) = TR(Total revenue)-TC(Total Cost)

where TC equals TVC(Total variable cost) plus TFC(Total fixed cost)

=> P= TR-(TVC+TFC)

Shut rule equation tells P<AVC, Multiplying both sides by Q(Quantity) we get

=>P*Q<AVC*Q

or

=>TR<TVC

Now suppose, an automobile firm who is running in losses has to decide whether to shut down or continue in business

TR($)	TVC($)	TFC($)	Profit	Shut Down or Continue
0	0	5,000	Profit=0-(0+10,000)=-10,000	Continue
10,000	15,000	5,000	Profit= 10000-(15000+5000)=-10000	Shut Down
10,000	10,000	5,000	Profit=10000-(10000+5000)=-5000	Can shut down or continue