The following table summarizes the short-run production function for your firm.

Question

The following table summarizes the short-run production function for your firm. Your product sells for $10 per unit, labor costs $40 per unit, and the rental price of capital is $10 per unit. Complete the following table, and then answer the accompanying questions.
L K Q MPL APL APK VMPL
0 5 0
1 5 20
2 5 60
3 5 120
4 5 160
5 5 180
6 5 190
7 5 190
8 5 180
9 5 160
10 5 120
11 5 60
(a) Which inputs are fixed inputs? Which are the variable inputs?


(b) How much are your fixed costs?


(c) What is the variable cost of producing 40 units of output?


(d) How many units of the variable input should be used to maximize profits?


(e) What are your maximum profits?


(f) Over what range of variable input usage do increasing marginal returns exist?


(g) Over what range of variable input usage do decreasing marginal returns exist?


(h) Over what range of variable input usage do negative marginal returns exist?

Explanation / Answer

completed table

L K Q MPL APL APK VMPL
0 5 0 0 0 0 0
1 5 20 20 20 4 $200
2 5 60 40 30 12 $400
3 5 120 60 40 24 $600
4 5 160 40 40 32 $400
5 5 180 20 36 36 $200
6 5 190 10 31.67 38 $100
7 5 190 0 27.14 38 0
8 5 180 -10 22.5 36 $100
9 5 160 -20 17.78 32 $200
10 5 120 -40 12 24 $400
11 5 60 -60 5.45 12 $600

where MPL = Q/L

APL = Q/L

APK = Q/K

VMPL = P*MPL where P=$10

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