1. Sketch the production isoquant for a production function that
takes two inputs (e.g. y = f[l,k]). Show the cost minimizing
combination of inputs by adding an isocost line to your
sketch.
(a) What is the relationship between the trs and the relative price
of one input compared to the other at the cost minimizing
combination of inputs?
(b) What does the assumption of a diminishing technical rate of substitution (trs) mean? (What does a diminishing trs mean imply for a firm’s willingness to pay for one input compared to another?)
2. A firm can choose between two techniques to produce
a good, each of which relies on labor, l, and capital, k, in fixed
proportions (fixed factor production). Technique 1 uses more labor
and requires only a minimal investment in machinery, while
technique 2 is more capital-intensive but requires little labor.
Use this information to answer the following questions.
(a) Sketch the production isoquants for each technique (assume both
produce the same level of output).
(b) Assuming the wage is low (i.e. the firm can save money by using technique 1), add the isocost curve that would represent the least-cost means of producing the good to your sketch.
(c) Is there a price at which the firm is ambivalent as to which
techniques to use? If so, add the corresponding isocost curve to
your sketch. What happens if the price of labor increases beyond
the price at which the firm might use either technique?
a. In the diagram, AB represents iso cost line and IQ1 is the isoquant representing the level of output produced by the economy. As the diagram clearly shows that the cost minimizing level of output occurs at point E1 where the slope of isoquant which is equal to technical rate of substitution is equal to the slope of iso cost lone which is the relative input price ratio. Thus, at the cost minimizing combination of inputs, TRS and relative price of one input compared to the price of another input are same.
b. The assumption of diminishing marginal technical rate of substitution means the rate at which one factor must decrease so that same level of productivity can be maintained when another factor is increased.
1. Sketch the production isoquant for a production function that takes two inputs (e.g. y = f[l,k]). Show the cost minim...
K Isoquant: Q 70 Tangency 8 Isocost: TC - $? 10 Figure 1. Isoquant and Isocost Price of L = $20; Price of K ? ; TC ? 16. Refer to Figure 1. If the price of capital increases while the price of labor is unchanged, which of the following is most accurate? In the new cost-minimizing input combination for producing Q-70, the labor input must be lower than 6. The isoquant of Q = 70 shifts inward. It is...
1. Suppose the production of digital cameras is characterized by the production function q F(K, L)- KL (MPL = K, MPK = L), where q represents the number of digital cameras produced. Suppose that the price of labor is $10 per unit and the price of capital is S1 per unit. (a) Graph the isoquant for q-121 000. (b) On the graph you drew for part a), draw several isocost lines including one that is tangent to the isoquant you...
Use the graph: Capital Isoquant 2 Isoquant 1 Isocost Labor 50 60 100 8. What is the MRTS between points A and B? 9. What is the MRTS between points B and C? 10. What is the slope of the isocost curve if wages=$300 a week and the rental price of capital is $300 per week? 11. Which isoquant curve represents higher output? 12. If Isoquant 1 represents output of 3000, what is the cost minimizing combination of inputs to...
TUTORIAL2 Chapter 7 Part 1 Key Concepts and Equations: Production Isoquant: shows all combinations of input quantities that yield the same level of output. Higher isoquant: higher level of output Marginal Rate of Technical Substitution: MRTS is the slope of the isoquant at any input combination. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. MRTS diminishes as we move down the isoquant from left to...
TUTORIAL2 Chapter 7 Part 1 Key Concepts and Equations: Production Isoquant: shows all combinations of input quantities that yield the same level of output. Higher isoquant: higher level of output Marginal Rate of Technical Substitution: MRTS is the slope of the isoquant at any input combination. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. MRTS diminishes as we move down the isoquant from left to...
TUTORIAL2 Chapter 7 Part 1 Key Concepts and Equations: Production Isoquant: shows all combinations of input quantities that yield the same level of output. Higher isoquant: higher level of output Marginal Rate of Technical Substitution: MRTS is the slope of the isoquant at any input combination. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. MRTS diminishes as we move down the isoquant from left to...
Isoquant: Q = 70 Tangency Isocost: TC = $? Figure 1. Isoquant and Isocost Price of L = $20; Price of K = ?; TC = ? 14. Refer to Figure 1. The intercept of the isocost on k axis is 10 15 20 33.33 Refer to Figure 1. When total cost is minimized for producing Q=70, the relative productivity ratio of capital to laboris O 2/1 1/2 4/5 5/4 17. Refer to Figure 1. It is observed that the...
For Question 1-4, use the following information: A firm's production function is gives as: q=3K0.6 L0.4 and its cost minimizing choice of inputs is L=250 and K=400 1. What is the value of MRTS at the firm's cost minimizing choice of input? 2. If the wage that the firm's pay to hire one unit of labor is 10, what is the user cost of capital? (Graph questions) <--- (Really important - please give clear steps and explanation) 3. Write down...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
1. Consider a steel firm that faces a convex isoquant production function where the inputs are labor and capital. The production function yields constant returns to scale. The firm is currently at a cost-minimizing combination of labor and capital for the desired level of output. Suppose the capital used in the production process emits low amounts of polluted wastewater into a nearby river. In order to promote the use of the environmentally friendly capital the government provides a unit subsidy...