Question 7 The production function is f(x1, x2)=x¹²₁x¹₂. 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 xı? Discuss what you observed in the graph that helped you to determine your answer. c. 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).
Question 7 The production function is f(x1, x2)=x¹²₁x¹₂. 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 xı? Discuss what you observed in the graph that helped you to determine your answer. c. 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).
Chapter1: Making Economics Decisions
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Transcribed Image Text:Question 7
The production function is f(x1, x2) = x¹/²₁x¹/22.
1X
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 x₁? 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).
d. If the price of factor 1 is $10, the price of factor 2 is $15, and the price of output is $20,
what is the short run profit maximizing choice of x₁? (The marginal product of factor 1 is
5
1/2
You will need to use this information to solve for the answer to c.) How did you
know that this was the answer? Use the graph from c) as part of your explanation.
C.
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