Question

A firm has a production function **Y =
(K ^{0.3})*(N^{0.7})**. Given this production
function, the marginal product of labor is given by

**Questions:**

**a) Calculate the optimal number of workers the firm will
hire. Round your answer to the closest integer.**

**b) Suppose that the government subsidizes employment by
0.05 per worker (s = 0.05). That is, the government pays the firm
0.05 units of consumption goods for each unit of labor that the
firm hires. Determine the effect of the subsidy on the firm’s
hiring decision, does the firm hire more or less workers than in
a).**

Answer #1

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Suppose that you have the following production function:
Y=9K0.5N0.5. With this production function the marginal product of
labor is MPN=4.5K0.5N-0.5 (hint: firms pay workers MPN so this
equals w). The capital stock is K=25. The labor supply curve is
NS=100[(1-t)]w]2 , where w is the real wage, t is the tax on
income, and hence (1-t)w is the after-tax real wage rate.
a) Graphically draw (a rough sketch is fine) of the labor market
and production function. Show graphically the...

1. Suppose a firm faces a fixed price of output, ? = 1200. The
firm hires workers from a union at a daily wage, ?, to produce
output according to the production function ? = 2?^1/2. There are
225 workers in the union. Any union worker who does not work for
this firm is guaranteed to find nonunion employment at a wage of
$96 per day.
a. What is the firm’s labor demand function?
b. If the firm is allowed...

A company’s production function is given by Y = A(40N –
N2 +100). Suppose the price of output is $6 per unit and A =1.
(Hint: you need to get MPN from the production function to solve
the questions below.)
What will be the demand for labor if the nominal wage is
$24?
What will be the demand for labor when the TFP is
increased such as A=2 (still assuming W=$24)?

The production function in an economy
is Y = 2(7N-0.02N2) With this production function, the
marginal product of labor is .mpn = 14 - .08N.
Labor Supply is , N8 =
88+2w,
Desired consumption is ,
Cd=100+0.8Y -5020r -.5G,
Desired investment is
Id=100-500r
Real money demand is Md/P =
Y-2000 (r+?e)
Other variables are expected inflation
?e=.05 , government purchases G = 200,
and money supply is M = 2100
1. Find the general equilibrium values of the real wage,...

There is a firm that produces using the production function
Y=A N - N2, where Y is output,
A is productivity, and N is employment. Firms
hire workers until the marginal product of labor is equal to the
wage rate, w. The supply of labor is Ns=0.5
w. Starting from A=2, the economy is hit by a
negative productivity shock that decreases A by 2%
(A changes from 2 to 1.96). What is the percentage change
in employment induced by...

Suppose the production function is Y=100(N-0.01N^2). And the
marginal product of labor is MPN=100-2N. The aggregate quantity of
labor supplied is NS=50+1.5w-Tr, where w is the real wage rate and
Tr = 20 is the lump-sum transfer that household received from the
government. The full-employment level of output is
less than or equal to 2,000
more than 2,000, but less than or equal to 2,500
more than 2,500, but less than or equal to 3,500
more than 3,500, but less...

1. The marginal product of labor falls as a firm hires more
hours because of:
A. falling output prices.
B. diminishing marginal product of labor.
C. rising wages.
D. changes in the cost of physical capital.
2. A decrease in the price of a good due to a fall in demand
will ultimately lead to
A. the market wage rate to decrease.
B. the firm hiring fewer workers.
C. the firm's demand for labor increasing.
D. the firm's demand for...

(a) Suppose the marginal product of labor is 8 and the marginal
product of capital is 2. If the wage rate is $4 and the price of
capital is $2, then in order to minimize costs should the firm hire
more workers or rent more capital? Please explain.
(b) Suppose the production function is given by Q = min{K, L}.
How much output is produced when 10 units of labor and 9 units of
capital are employed? Please explain.

Suppose the production function is Y=100(N-0.01N^2). And the
marginal product of labor is MPN=100-2N. The aggregate quantity of
labor supplied is NS=50+1.5w-Tr, where w is the real wage rate and
Tr = 20 is the lump-sum transfer that household received from the
government. The equilibrium real wage is
less than or equal to 10
more than 10, but less than or equal to 15
more than 15, but less than or equal to 20
more than 20, but less than...

Given the Production Function of a perfectly competitive firm: Q
= 30L + 12L2 – 0.5L3 , where Q = Output and L = labor input
a. At what value of L will Diminishing Returns take effect?
b. Calculate the range of values for labor over which stages I,
II, and III occur?
c. Suppose that the wage rate is $30 and the price of output is
$2 per unit. How many workers should the firm hire?
d. At what...

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