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