1. (Textbook problem 2, page 103) An economy has the production function Y=0.2(K+√N). In the current period, K = 100 and N = 100. a. Graph the relationship between output and capital, holding labor constant at its current value.
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- What is a production function?1. (Textbook problem 2, page 103) An economy has the production function Y=0.2(K+√N). In the current period, K = 100 and N = 100. a. Graph the relationship between output and capital, holding labor constant at its current value. b. What is the marginal product of capital? c. Does the marginal product of capital diminish? d. Graph the relationship between output and labor, holding capital constant at its current value. e. Does the marginal productivity of labor diminish?3. Imagine we live in a classical world. Suppose that the production function is Y = L²K², where L is the amount of labor and K is the amount of capital. The economy has 100 units of labor and 100 units of capital. a. Does the production function show Constant Returns to Scale? Why? b. Derive an expression for the marginal product of labor. Is the marginal product of labor diminishing? How does an increase in the amount of capital affect the marginal product of labor? Explain. What are the real wage and rental price of capital? d. What is the income share paid to labor? What is the income share paid to capital? C.
- 1. Imagine an economy with a constant returns to scale production function. Answer the following: (a) Suppose this economy has 3000 units of physical capital, with workers having 200 years of education, and they work 5000 hours. Their output is worth $10,000. Now imagine the same economy has 6000 units of physical capital, 400 years of education, and the workers work 10000 hours. What is their output now? (b) b) Suppose this economy has 3000 units of physical capital, with workers having 200 years of education, and they work 5000 hours. Their output is worth $10,000. Now, their physical capital grows to 6000 units, but the other two inputs remain the same. Provide a range for what the economy's output might be. That is, what is the lower bound, and what is the upper bound for this economy's output? (c) Suppose this economy has 3000 units of physical capital, with workers having 200 years of education, and they work 5000 hours. Their output is worth $10,000. Call this Country A. Now…5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?3. What are the 2 variables that the Production Function is analyzing/graphing? Why does the production function diminish over time?
- 4) Suppose you are a hard-working software engineer that works 2000 hours a year, which you allocate between meetings (m), learning activities (I) and working effort (e) doing actual coding tasks (m + 1 + e = 2000). a. Write down your personal production function f (m, 1, e). Briefly describe how your output depends on the three activities. b. Does your production function exhibit increasing, decreasing or constant returns to scale (at all or some output levels)? Explain. c. Suppose a new technology doubles the productivity of your coding hours but requires you to spend X hours to adopt the technology (reducing your available work hours to 2000-X). What is the maximum X that makes adopting the technology worthwhile in the first year?1. Consider this simplified sequence: A farmer starts with a unit of wheat and sells it to a miller for 20 cents. The miller grinds it into flour and sells it to a baker for 50 cents. The baker converts all the flour into a loaf of bread and sells it to a grocer for $2.00. The grocer then sells that bread to a customer for $3.35. a) What is the total value added by the grocer? b) What is the total value added by all these stages of production? I c) How much does GDP increase?An economy has the following Cobb-Douglas production function: ?=100?^(1/3)?^(2/3) . The economy has 125 units of capital and 64 units of labor. d. Calculate the marginal product of capital MPK. e. Calculate the marginal product of labor (MPL).
- 1. We have assumed that the production function simultaneously has constant returns to scale and diminishing marginal products. What do each of these terms mean? Is it a contradiction for a production function to feature constant returns to scale and diminishing marginal products? Why or why not?1. Suppose the production function is Q = 8L + 15K where Q is the quantity of output, L is the quantity of labor used in production, and K is the quantity of capital used in production. What can be said about this production function? It has Decreasing Returns to Scale It has Constant Returns to Scale It has Increasing Returns to Scale There isn’t enough information to determine the Returns to Scale for this production function 2. You’re dreaming of what to do during a nice summer day. You could mow the lawn which you would pay someone $15 to do for you. You could go for a walk which you value at $11. You could also take a nap and ignore everyone and everything else which you would pay $29 to do. If you to take a nap, what is your opportunity cost? Group of answer choices $29 $26 $15 $111a. Define constant, decreasing and increasing returns to scale. b. A technology can exhibit constant returns to scale and diminishing marginal product to each factor. True or False? Briefly explain. c. A technology can exhibit different kinds of returns to scale at different ranges of production. True or False? Briefly explain.