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Question 1 A firm has a monopoly in the production of antimacassars. Its factory is located in a town where no other industry exists and the labour supply is W = 10 + 0.1L, where W is the daily wage and L is the number of persondays of work performed. The firm production function is Q = 10L, where L is daily labour supply and Q is daily output. The demand curve for the good is P = 41 ? Q 1,000 , where P is the price and Q is the number of sales per day. a) Find the profit-maximizing output for the firm. (Hint: make substitutions so that you can write both the firm’s revenue and total costs as a function of output, Q). b) How much labour does it use? What is the wage rate that it pays? c) What is the price of the good? How much profit is made?

Answer #1

A firm has a daily production function q = 2.5L^1/3K^1/3.
Currently, the firm rents 8 pieces of equipment. The amount of
equipment is fixed in the short run. The unit wage rate is $25
while the rental cost of capital is $100.
Find the short run production function.
Find the number of workers the firm wishes to employ to produce
q units (the short run conditional demand for labor).
Find the firm’s short run total cost
Find the firm’s short...

1. A firm production function is given by q(l,k) =
l0.5·k0.5, where q is number of units of
output produced, l the number of units of labor input used and k
the number of units of capital input used. This firm profit
function is π = p·q(l,k) – w·l – v·k, where p is the price of
output, w the wage rate of labor and v the rental rate of capital.
In the short-run, k = 100. This firm hires...

4.1
Consider a profit-maximizing firm with the production function,
q(L,K). Capital is fixed at K0. Explain what happens to
demand for L and to profits, p, under the
following scenarios:
(a) w, the price of L rises
(b) v, the price of K rises
(c) p, the price of the output rises

Suppose you own a firm that producing shoes using both capital
and labor. The production function is q=f(K, L)=0.5K2 L4 . In long
run both capital (K) and labor (L) are variable. Price for each
pair of shoes is $50 (p=50), the wage rate is 0.04 (w=0.04) and the
rental price for capital is 1 (r=1). Given those output and input
prices, what is the profit maximizing input level of K and L (K*
& L* )?

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...

1. A monopsonist has the production function
Q=4⋅L
and faces the following labor supply and product demand
equations respectively.
W=2+0.05⋅L
P=10−0.025⋅Q
How much labor should the firm hire in order to maximize profits
if they mark their price 300% above marginal cost? Answer is not
10
2.
A monopsonist has the production function
Q=4⋅L
and faces the following labor supply and product demand
equations respectively.
W=2+0.05⋅L
P=10−0.025⋅Q
What wage rate should the firm pay in order to maximize profits
if...

Consider a firm using quantities L1 and L2 of two kinds of
labour as its only inputs in order to produce output Q=L1+L2. Thus,
each unit of labour produces one unit of
output. Suppose that we also have two segmented labor markets,
with the following inverse labor supply functions.
w1=α1+β1L1
w2=α2+β2L2
which shows the wage that must be paid to attract a given labor
supply. Assume that the firm is competitive and take price of
output P as given. (α1,...

Consider a price-taking firm that produces widgets with only
labour input. Let the relation between widget output and labour
input be the function f(z), where z is labour input. Denote the
price of widgets by p and the wage rate (the price of labour) by w;
assume both p and w are positive and beyond the firm’s control.
Assume the firm chooses labour input to maximize profits. Denote
the labour demand function by z(w, p), the output supply function
by...

Consider the following firm with its demand, production and cost
of production functions:
(1) Demand: Q = 230 – 2.5P + 4*Ps + .5*I, where Ps = 2.5, I =
20.
(2) Inverse demand function [P=f(Q)], holding other factors (Ps
= 2.5 and I =20) constant, is, P=100-.4*Q.
(3) Production: Q = 1.2*L - .004L2 + 4*K - .002K2;
(4) Long Run Total Cost: LRTC = 2.46*Q + .00025*Q2 (Note: there
are no Fixed Costs);
(5) Total Cost: TC =...

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