Question

1. Suppose a short-run production function is described as Q = 30L - 0.05L^2 where L is the number of labors used each hour.

a. Derive the equation for Marginal Product of Labor

b. Determine how much output will the 200th worker contribute:

c. Determine the amount of labor (L) where output (Q) is maximized (known as Lmax):

d. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?

e. Given your answer to part b, what output (Q) will the firm produce?

f. Assuming no other cost than labor costs, what is the profit at the level of labor computed in part c:

g. Suppose that the marginal revenue (price) for the product is unchanged at $5, but that the cost of hiring labor increases to $45 per hour. How many labor units (L) will the firm employ?

h. Suppose that labor costs is back to $40 but the marginal revenue (price) received per unit of output increases to $8. How many labor units (L) will the firm now employ?

i. In terms of the demand (curve) for labor, how would we see (what is the difference between) the changes in parts g and h above?

j. Using the terminology from class and this question, briefly explain why manufacturing jobs such assembling TVs are no longer highly compensated (and therefore moved overseas).

Answer #1

1. Suppose a short-run production function is described as Q =
2L – (1/800)L^2 where L is the number of labors used each hour. The
firm’s cost of hiring (additional) labor is $20 per hour, which
includes all labor costs. The finished product is sold at a
constant price of $40 per unit of Q.
a. How many labor units (L) should the firm employ per hour
b. Given your answer in a, what is the output (Q) per hour...

1. Suppose a short-run production function is described as Q =
2L – (1/800)L2 where L is the number of labors used each hour. The
firm’s cost of hiring (additional) labor is $20 per hour, which
includes all labor costs. The finished product is sold at a
constant price of $40 per unit of Q.
a. How many labor units (L) should the firm employ per hour:
b. Given your answer in a, what is the output (Q) per hour:...

Suppose a short-run production function is described as Q = L –
(1/400)L2where L is the number of labors used each hour.
The firm’s cost of hiring (additional) labor is $16 per hour, which
includes all labor costs. The finished product is sold for $40 per
unit of Q.
c. How many labor units(L)
should the firm employ per hour if they want to maximize profit?
L = 120
f. Suppose that the price of the product is unchanged...

Suppose the final goods production function is fixed-proportion,
Q = f(E, L) = min{E,L}, where Q is output level, E is energy input
and L is the labor in- put. Let m be the marginal cost of energy
per unit and w be the price of labor per unit. Suppose the demand
function for final good is P = 1 - Q
a). (10) Suppose energy and final good are produced by two
different firms. Derive the cost function of...

Suppose the final goods production function is fixed-proportion,
Q = f(E, L) = minf(E,L), where Q is output level, E is energy input
and L is the labor in- put. Let m be the marginal cost of energy
per unit and w be the price of labor per unit.
Suppose the demand function for final good is P = 1 - Q:
a). (10) Suppose energy and nal good are produced by two
different rm. Derive the cost function of...

Suppose a firm’s long-run production function is given by
Q=K^0.25 L^0.25 ,where K is measured in machine-hours per year and
L is measured in hours of labor per year. The cost of capital
(rental rate denoted by r) is $1200 per machine-hour and the cost
of labor (wage rate denoted by w) is $12 per hour.
Hint: if you don’t calculate the
exponential terms (or keep all the decimals when you do), you will
end up with nice numbers on...

Suppose a firm’s production function is given by Q = L 1/2 , K
1/2.
a) Suppose the firm has a fixed cost FC=6, the price
of labor is w = 64 and the price of capital is r = 4. Derive the
firm’s total cost function, TC(Q).
b) What is the firm’s marginal cost?
c) Graph the firm’s isoquant for Q = 20 units of
output. On the same graph, sketch the firm’s isocost line
associated with the total...

A firm produces an output with the production function Q = KL,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal
products for this production function are MPK= L and MPL= K. The
factor price of K is 4 and the factor price of L is 2. The firm is
currently using K = 16 and just enough L to produce Q = 32....

10. Suppose the short-run production function is q =
L.5
.
If the marginal cost of producing the tenth unit is $5, what is
the wage per unit of labor?
A.$1
B.$0.25
C.$0.5
D.It cannot be determined without more information

A firm has the following short run total product
curve:
TPL = Q = 10.5L + 1.5L2 - .0625L3,
where labor, L, is the only variable input and TPL is
the total output produced per day. Assume the firm faces a fixed
price of $16.00 per unit for its output. Also assume that only
whole units of output are possible.
a.If the firm must pay a market-determined wage rate of
$60.00 per day for each unit of labor hired, how...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 12 minutes ago

asked 15 minutes ago

asked 20 minutes ago

asked 27 minutes ago

asked 37 minutes ago

asked 48 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago