Final answer:
The isoquant curve for Y=K¹/³L²/³ at Y=2 is a graph that represents all combinations of labor and capital that produce 2 units of output. By calculating pairs (K, L) for various values of K, the curve can be plotted to show the trade-off between capital and labor. This concept reflects adjustments firms make in response to changes in input costs, similar to historical trends.
Step-by-step explanation:
To plot the isoquant curve for the production technology given by Y=K¹/³L²/³ at Y=2, we first set the production function equal to 2 and then solve for L in terms of K. This gives us the relationship between the quantity of labor L and capital K that yields an output level of 2 units. An isoquant curve represents all combinations of capital and labor that can produce the same output level, in this case, Y=2.
We can write the equation in terms of L as L = (2/K¹/³)¹/²³. By choosing various values of K, we can calculate corresponding values of L to plot on the graph. Once we have a set of (K, L) pairs, these points can be plotted to draw the isoquant. For example, if K=1, then L = 2³ = 8, giving us the pair (1, 8). If K=8, then L = (2/2)³ = 1, giving us the pair (8, 1). Plotting several such points forms the isoquant curve for Y=2.
This isoquant can be illustrated on a graph with the capital on the horizontal axis and labor on the vertical axis. Such curves are downward sloping, reflecting the trade-off between capital and labor: as less capital is used, more labor is required to produce the same amount of output, and vice versa. This is consistent with the concept of marginal rate of technical substitution, which measures the rate at which labor can be substituted for capital without changing the output level. The isoquant will also reflect the context of the question. If the cost of capital has increased, firms would shift towards using more labor. This is similar to the historical economic situation in the United States during the 1970s when, due to cost pressures, firms sought to optimize the mix of inputs to maintain profitability in response to shifting demand.