ECO 3320 Exam #3
Average cost (AC)=
AFC+AVC C/q
Economies of scale exist whenever long-run average costs:
decrease as output is increased
Production Function
q=f(L,K)
Constant returns to scale exist when long-run average costs:
remain constant as output is increased
An isocost line:
represents the combinations of K and L that cost the firm the same amount of money
Output
service or physical product
Suppose the cost function is C(Q) = 50 + Q − 10Q2 + 2Q3. What is the variable cost of producing 10 units?
$1010
Suppose the cost function is C(Q) = 50 + Q − 10Q2 + 2Q3. What is the total cost of producing 10 units?
$1060
Suppose the cost function is C(Q) = 50 + Q − 10Q2 + 2Q3. What is the marginal cost of producing 10 units?
$401
Suppose the cost function is C(Q) = 50 + Q - 10Q^2 + 2Q^3. What are the fixed costs?
$50
Capital
-K -Land, buildings, equipment
Labor
-L -skilled and less-skilled workers
Materials
-M -natural resources, raw materials and processed products
equality
-MPL/MPK=change in K/change in L=MRTS
What is the slope of an isoquant?
-Marginal Rate of Technical Substitution (MRTS) -how many units of capital the firm can replace with an extra unit of labor while holding output constant.
Isoquants:
-slope downward -do not cross -the father from the origin the greater the level of output LR
If the production function is Q = K.5L.5 and capital is fixed at 1 unit, then the average product of labor when L = 25 is:
1/5
For the cost function C(Q) = 100 + 2Q + 3Q2, the marginal cost of producing 2 units of output is:
14
Given the Leontief production function Q=min{5.5K, 6.7L}, how much output is produced when K=40 and L=35?
220
Given the production function Q = min{4K, 3L}, what is the average product of capital when 8 units of capital and 16 units of labor are used?
4
Suppose the production function is given by Q = 3K + 4L. What is the average product of capital when 10 units of capital and 10 units of labor are employed?
7
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?
9
Production Process
A firm uses a technology or production process to transform inputs or factors of production into outputs
Average fixed cost (AFC)
Declines continuously as output is expanded
Average Fixed Cost (AFC)=
FC/q
Total cost (TC)=
Fixed Cost (FC) + Variable Cost (VC)
Perfect compliments
L shaped
slope of isoquant
MRTS=MPL/MPK
How to calculate MRTS
MRTS=change in K/ change in L
Firm managers should use inputs at levels where the:
Marginal benefit equals marginal cost and value marginal product of labor equals wage
Production Function
Maximum quantity of output that can be produced with different combinations of inputs, given current knowledge about technology and organization
APL=
Q/L
The Cobb-Douglas production function is:
Q=K^aL^b
Which of the following conditions is true when a producer minimizes the cost of producing a given level of output?
The MRTS is equal to the ratio of input prices, and the marginal product per dollar spent on all inputs is equal
It is profitable to hire labor so long as the:
VMPL is greater than wage
Average Variable Cost (AVC)
Variable cost (VC)/q
Isocost line
all combinations of inputs that have the same total cost C=wL+rK w=wages, r=cost of unit of capital
Marginal Cost (MC)=
amount by which a firms cost changes if the firm produces one more unit of output CHANGE in C/ CHANGE in q
Sunk costs are those costs that:
are forever lost after they have been paid
The difference between average total costs and average variable costs is:
average fixed cost
Slope of an isocost line
change in K/change in L=-w/r
MPL=
change in Q/change in L
Marginal Cost (MC)=
change in VC/change q
Imperfect substitutes
convex curved
Explicit Costs
direct, out of pocket payments for labor, capital, energy and materials
Suppose the long-run average cost curve is U-shaped. When LRAC is in the increasing stage, there exist:
diseconomies of scale
As long as marginal product is increasing, marginal product is:
greater than average product
The Leontief production function
implies inputs are used in fixed proportions
The short term is defined as the time frame:
in which there are fixed factors of production
If MPL/MPK is less than w/r then MPL/w is less than MPK/r so
increase K, decrease L
If MPL/MPK is greater than w/r then MPL/w=MPK/L so
increase labor decrease K
Long-run
inputs in the long run are all variable--varied
The marginal cost curve:
intersects the ATC and AVC at their minimum points
If the marginal product per dollar spent on capital is less than the marginal product per dollar spent on labor, then in order to minimize costs the firm should use:
less capital and more labor
Perfect substitutes
linear lines
Variable factors of production are the inputs that a manager:
may adjust in order to alter production
Suppose the marginal product of labor is 10 and the marginal product of capital is 8. If the wage rate $5 and the price of capital is $2, then in order to minimize costs the firm should use
more capital and less labor
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 the firm should use:
more labor less capital
The isoquants are normally drawn with a convex shape because inputs are:
not perfectly substitutable
With a linear production function there is a:
perfect substitutable relationship between all inputs
You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w = $40, r = $100, MPL = 20, and MPK = 40 the firm:
should use more L and less K to cost minimize
Short-run
so brief at least one factor of production is fixed or variable inputs
What does an isoquant show?
the efficient combinations of labor and capital that can produce the same level of output
The long run is defined as:
the horizon in which the manager can adjust all factors of production
Implicit Costs
the opportunity costs of a resouce
An isoquant defines the combination of inputs that yield the producer:
the same level of output
The marginal product of an input is defined as the change in:
total output attributable to the last unit of an input
Accounting Profit
total revenue - explicit costs
MRTS=
w/r
