Question

Problem #3: Long-Run Labor Dernand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produe Y units of output according to the following production function Y = 30K + 10L The firm wants to produce 600 units of output 1. Draw the ot that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical axis. 2. The shape of the isoquant els us about the relationship between the two inputs in production How substitutable are L and K in the production of Y? In particular, how many units of L can be replaced by one unit of K without affecting the evel of output? 3. Is this isoquant convex (bowed toward the origin)? 4. In class, we said that isoquants are cox under our "standard assumptio" To see which standard assumption is violated in this case, hold K fixed at some level (for con venience, suppose K is fixed at zero). Graph Y as a function of L for L-0,5 is the change in Y (ΔΥ) when L increases by 1 unit (AL-1)? different from the "standard assumption" about the MPL we made in class? 5. By looking at your graph, determine the marginal product of labor (MPL). That is, what 6. How does the marginal product of labor (MPL) change as L increases? How is this 7. Suppose the firm can choose whatever combination of capital (K) and labor (L) it wants to produce 600 units. Suppose the price of capital is S1,000 per machine per week. What combination of inputs (K and L) the firm use if the weekly salary of each worker is $400?

Answer 1

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