Question 7 The production function is f(x,x)=x¹²₁x¹2₂ a. In the short run the amount of factor 2 (x2) is 100 units. Write down the short run production function and draw a graph of it with output on the vertical axis and the amount of factor 1 on the horizontal axis. b. How does the marginal product of x1 in the graph you drew in a) change with the amount of xi? Discuss what you observed in the graph that helped you to determine your answer. Write out the equation for an iso-profit line and add it to the graph you drew in part (a). Show how you derive the iso-profit line from a profit function that depends on output (y) and the amount of the inputs (x1 and x2). c.

Grease Tech produces oil changes. The production of oil changes reles on both capital (K) and labor (L) and is combined in the following production function F (K, L) = KILL Take the derivative of this production function with respect to capital. What is the marginal product of capital evaluated at (le. just plug in the numbers) 64 units of capital used and 16 units of labor?

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Could you please help me with this question? Thank you!

GM cuts jobs at its Australian manufacturing unit GM will cut 500 jobs, or about 12% of its workforce, at its Australian plant because of a sharp fall in demand for its locally-made "Cruze" small car. Source: The Wall Street Journal, April 8, 2013 As GM cuts its workforce, how will the marginal product and average product of a worker change in the short run? Suppose that before the cuts the marginal product of GM workers is below their average product. As the number of workers decreases, the marginal product of a GM worker and the average product of a GM worker in the short run. increases; decreases does not change; does not change decreases; decreases increases; increases decreases; increases

answer question d Q5. Jason is running a cleaning business, there are available labours (L) and machines (M) for Jason to use as inputs to produce cleaning service for his clients. a) Suppose Jason must use both labours and machines without any specific ratio to complete the service for his clients, please write down the general production function formula for Jason. hint: you could use any letter if you want] b) Under the function form of a), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) equals to 2, how do you interpret it? c) Assume Jason now can use only single input, either labour or machine to complete the service, please write down the general production function formula for Jason. hint: you could use any letter if you want] d) Under the function form of c), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) is always larger than the market price ratio between labour and machine (w/r), what should Jason do? why?

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Sandwiches, a sandwich shop, has the following marginal product curve (labelled MP) for its hourly productions hourly production.

2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).

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 $11