Question

Suppose long-run production of automobile per day is given by qA = KL (for example, if K = 7 and L = 3, then 21 autos will be produced daily).

a. The input bundle given by (K = 5, L = 5) is sufficient to produce 25 units of output. Plot the 25-unit isoquant by identifying four additional input bundles sufficient to produce 25 units of output (use exact values for the four additional input bundles and label them and their corresponding quantities of inputs).

b. In the short run (holding K fixed) does this production function exhibit diminishing marginal returns, constant marginal returns, or increasing marginal returns? (Explain your answer with an example, like K =5)

c. In the long run (allowing both K and L to change) does this production function exhibit decreasing returns to scale, constant returns to scale, or increasing returns or scale? (Explain your answer with an example.)

Answer 1

a) Production function: qA=KL

Units of capital	Units of labour	Output produced (qA=KL)
5	5	25
1	25	25
25	1	25
10	2.5	25
2.5	10	25

Out of all the values possible to obtain 25 units of output produced, five values are shown in the above table and same is plotted on the graph given below. On the y-axis, units of capital is shown and on x-axis, units of labour is shown. IQ is the 25-unit isoquant showing different input bundles sufficient to produce 25 units of output.

b) Production function: qA=KL
In Short Run, capital is fixed at say K=5 while labour is variable. Now suppose L =2.
qA = (5)(2)=10 units
Suppose labour increases to L=4 while capital is constant at K=5
qA = (5)(4) = 20
Now, it can be seen that with constant capital, when the labour is doubled (2 to 4), output is also doubled (10 to 20). This implies that the production function exhibits constant marginal returns.

c) Production function: qA=KL
In Long Run, both capital and labour are variable. Suppose capital is at say K=2 while labour is at L =2.
qA = (2)(2)=4 units
Suppose capital increases to K=4 and labour increases to L=4
qA = (4)(4) = 16
Now, it can be seen that when both the labour and capital are doubled (2 to 4), output is more than doubled (4 to 16). This implies that the production function exhibits increasing returns to scale.