Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
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Question
Chapter A, Problem 4P
a)
To determine
The graphical representation of the relationship between Y, K, and N when N = 100.
b)
To determine
The change in the function and graph relating Y, N, and K when N rises to 200 and fall to 50.
c)
To determine
The elasticity of Y with respect to K and elasticity of Y with respect to N.
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A firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram
we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice
that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew
Select one:
O a. is vertical.
b. is horizontal.
c. is a ray through the origin with slope 3.
d. is a ray through the origin with slope 4.
O e. has a negative slope.
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function.
S- 20100.70
In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100.
(a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost.
Min
s.t.
-55,000
L.C20
(b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.)
at (L. C) =
A custom motorcycle company can produce more motorcycles if it has more workers. The company has experimented with hiring workers in teams of four and has come up with the following table relating the number of workers to the companies annual production.
Using the straight line tool, graph the production function based on the information given. Construct the curve using four line segments joined end to end. Do not graph the individual points
Chapter A Solutions
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