Consider a manufacturing firm operating a given scale of plantcontaining some assembly equipment. Assume that the only input that the firm can change the amount of that can be used during the time period considered is labor (L).
Assume that the production function between Labor (L) and Total Product (Q) is as given in the first two columns of the table below.
Labor (L) Total Product (Q)
1 15
2 36
3 57
4 72
5 75
6 60
7 21
Assume that depreciation on the plant and equipment, interest on borrowed money, property taxes, insurance, etc., i.e., Total Fixed Costs (TFC), are $250, and that the price of a unit of labor (PL) is $125.
A. Calculations For each level of output (Q) shown in the second column in the above table, calculate a value for each of the following cost measures: Total Fixed Cost (TFC), Total Variable Cost (TVC), Total Cost (TC), Average Fixed Cost (AFC), Average Variable Cost (AVC), Average Total Cost (ATC) and Marginal Cost (MC). [Note: In calculating the average cost measures be sure to divide the corresponding total cost measure by Q and NOT by L.] Each MC calculation made using the discrete formula may be placed on the row corresponding to the higher of the two levels of output used in the calculation. For example, the MC calculated between 72 and 75 units of Q using the discrete formula may be placed on the row corresponding to 75 units of Q.
B. 1. What happens to the value of each of the total cost measures, i.e., TC, TVC, and TFC, as Q increases (increases, decreases, remains constant?).
2. What happens to the value of AFC as Q increases?
3. How long does AFC decrease?
4. AVC decreases over the range of output from _____ to _____. Over this range of output what is happening to the values of AFC and ATC as output increases?
5. AVC increases over the range of output from _____ to _____. Over this range of output what is happening to the values of AFC and ATC as output increases?
6. ATC reaches a minimum at a level of output approximately equal to _____ . AVC reaches a minimum at a level of output approximately equal to _____.
7. Pick a level of Q for which MC < ATC. If Q were to increase, the value of ATC (increases, decreases, stays the same?)
8. Pick a level of Q for which MC > ATC. If Q were to increase, the value of ATC (increases, decreases, stays the same?)
9. Over that range of labor usage throughout which MP decreases as L increases, for the corresponding range of output, as Q increases, MC (increases, decreases, remains constant?) Explain.