Problem Set 2, Eco 103  Due date, Oct. 20th

1.  Production and Costs  ( 10 pts ):  You must show all of your work where calculations are required and you must include a brief explanation of approximately 20-30 words for written answers to receive full credit:

a.    Marginal and Average Product (10 pts):  Suppose you are given the following information for Acme Spring Corp., a firm that produces large industrial springs.

Inputs of labor    Total Product    Marginal Product (MP)
0    0    —
1    24
2    50
3    74
4    94
5    110
6    122
7    130
8    134
9    134
10    132

i)    Fill in the column for MP to complete the table above.  Explain at least one calculation completely in order to receive credit.  6 pts

ii)    Does this production data illustrate the law of diminishing returns?  Why or why not? 2 pts

iii)    If diminishing returns are present, at what level of labor input do they begin?  Explain your answer.  2 pts

2.  Short Run Production Costs (10 pts):  Suppose you are given the following information for the Wee Widget Company.  Assume Total Fixed Costs (TFC) equal $12 and Total Variable Costs (TVC) are as shown below:

Output (Q)    Total Fixed Costs (TFC)    Total Variable Costs (TVC)    Total  Costs (TC)    Marginal Costs (MC)    Average Fixed Costs (AFC)    Average Variable Costs (AVC)     Average Total Costs (ATC)
0        $0        —    —    —    —
1        $8.00
2        $14.00
3        $18.00
4        $20.00
5        $24.00
6        $30.00
7        $38.00
8        $52.00
9        $76.00
10        $112.00

Fill in columns for TFC, TC, MC, AFC, AVC, and ATC to complete the table above.  AGAIN, MAKE SURE TO EXPLAIN AT LEAST ONE OF EACH CALCULATION IN EACH COLUMN.  ROUND ANSWERS TO 2 DECIMAL POINTS.

3.  Profit Maximization in the Short Run (10pts):  Consider the following data for a firm, showing output and total costs.  Assume this firm seeks to maximize profits and uses the MR=MC RULE to find its profit maximizing (or loss minimizing) level of output.  Total fixed costs (TFC) for this firm $235.  You must show all of your work where calculations are required and you must include a brief explanation of approximately 20-30 words for written answers to receive full credit:

Output (Q)    Total Costs (TC)    Marginal Cost (MC)
0    $235    —
1    $300
2    $355
3    $405
4    $452
5    $500
6    $552
7    $610
8    $680
9    $760
10    $860
11    $990
12    $1,150
a.    Fill in the column for MC to complete the table above (2pts).  Explain the calculation.

b.    (4pts)  Suppose that this company can sell all units of their product at a price of $130.00.   Thus, marginal revenue, MR, equals $130.

i)    What is the profit maximizing (loss minimizing) level of output for this firm in the short run?
ii)    Calculate the total economic profit (or loss) that this firm would receive at this particular level of output. You must show all of your work to receive full credit
iii)    Should this firm continue to produce or should it shut down in the short run?  Why?

c.    (4pts) Assume instead that this firm can sell all units at a price of $70 . Thus $70 is MR, marginal revenue.

i)    What is the profit maximizing (loss minimizing) level of output for this firm in the short run?

ii)    Calculate the total economic profit (or loss) that this firm would receive at this particular level of output. You must show all of your work to receive full credit

iii)    Should this firm continue to produce or should it shut down in the short run?  Why?