Production function: Y = 30K + 10L
(1)
When Y = 600, we get
600 = 30K + 10L
60 = 3K + L (Dividing by 10)
When L = 0, K = 60/3 = 20 (Vertical intercept) and when K = 0, L = 60 (Horizontal intercept).
In following graph, Q0 is the isoquant. When production function is linear, isoquants are straight lines touching both axes.
(2)
Since production function are linear, K and L are perfect substitutes. The production process requires 10N units of labor or 30N units of capital for an output level of Q. So,
30 units of K can be substituted for 10 units of L.
1 unit of K can be substituted for (10/30) = (1/3) unit of L. This is the substitution ratio between K and L.
(3)
Since the isoquant is a straight line, it is not convex. A convex isoquant requires a non-constant Marginal rate of technical substitution (MRTS) but for a linear isoquant, MRTS is constant (MRTS = slope of isoquant).
(4)
When K = 0, substituting in production function we get
Y = 10L
When L = 0, Y = 10 x 0 = 0
When L = 1, Y = 10 x 1 = 10
When L = 2, Y = 10 x 2 = 20
When L = 3, Y = 10 x 3 = 30
When L = 4, Y = 10 x 4 = 40
When L = 5, Y = 10 x 5 = 50
The following graph plots the value of Y for values of L.
NOTE: As per Answering Policy, 1st 4 parts are answered.
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production...
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...
Please show all work. Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce 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 isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and...
Please show all work. Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce 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 isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and...
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