Question

**Suppose a typical firm uses K and L inputs that
have per unit costs of w and c, respectively. Initially, the firm
is in LR equilibrium when input prices are w=6 and c=4, then
suppose input prices change to w=4 and c=2.**

**How will the substitution effect impact the
firm’s utilization of K and L?**

**How will the scale effect impact the firm’s
utilization of K and
L?**** **

**Overall, can we say with any certainty whether
the overall utilization of K and L will increase, decrease, or
remain the same? Explain.**

**Do NOT wait until the last minute to answer
questions 15–18 because a new labor market report will be released
8:30 am EST on Friday, March 2 and some of these data may no longer
be visible on the summary table.**

**Go to the Bureau of the Labor Statistics (
HYPERLINK "http://www.bls.gov/" http://www.bls.gov/) and examine
the data in summary Table A: on the BLS front page, right side
column, “Latest Numbers”, Unemployment Rate, click on the icon that
looks like a report (not the graph), click on Summary Table A.)
Support your answers with data.**

Answer #1

Initially firm is in long run equilibrium and we know long run equilibrium is at a point where MRTS=MPL/MPK=W/C

Thus initially MPL/MPK=6/4=3/2

When W/C changes to 4/2=2

MPL/MPK also needa to be equal to 2.

Thus MPL needs to rise and MpK needs to decrease.

MpL will increase only when Labor is decreased because of law of diminishing returns and MPk will decrease only when K is increased. Thus at W=4 and C=2, labor needs fo be decreased and capital needs to be increased in order to achieve new long run equilibrium.

a. A firm uses only two inputs: capital (K) and labor
(L).Currently, the firm’s choice of capital (K) and labor (L) are
such that marginal product of capital is 80 and the marginal
product of labor is 10. If one put Labor on the x-axis, derive the
slope of the firm’s isoquant given the information above (include
the formula you use to do this).
b. The price of capital (Pk) is $40 and the price of labor (PL)
is $20....

A firm produces output (y), using capital (K) and labor (L). The
per-unit price of capital is r, and the per-unit price of labor is
w. The firm’s production function is given by, y=Af(L,K), where A
> 0 is a parameter reflecting the firm’s efficiency.
(a) Let p denote the price of output. In the short run, the
level of capital is fixed at K. Assume that the marginal product of
labor is diminishing. Using comparative statics analysis, show that...

A firm uses only two inputs L and K, which have prices PLand PK.
Its production function is q = 4L3K2
a. (3) Derive themarginal product of K and L (you can leave it
unsimplified).
b. (3) Derive the firm’s marginal rate of substitution including
the formula you use (you can leave it unsimplified)..
c. (3) Assume now instead that q = LK. Using this, solve for
K(as a function of L and q).
d. (8) Assume PL= 2, Pk=...

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