Deck 7: Production Cost: Many Variable Inputs

Question 1

The demand for inputs is conditional on the:

A)consumers' choice problem.
B)marginal rate of technical substitution.
C)supply of inputs.
D)level of output.

Answer 1

level of output.

Question 2

For any homothetic production function:

A)the output- expansion path is convex.
B)the output- expansion path is linear.
C)isoquants share a common point.
D)the output- expansion path passes through the origin of the input space.

Answer 2

the output- expansion path is linear.

Question 3

Increasing returns to scale are said to occur when:

A)the scale elasticity of output is positive.
B)the slope of the production function exceeds 1.
C)the scale elasticity of output exceeds 1.
D)the scale elasticity of output is increasing.

Answer 3

the scale elasticity of output exceeds 1.

Question 4

For a firm that experiences decreasing returns to scale over the entire range of output:

A)the SRMC curve is downward- sloping.
B)the LRAC curve is upward- sloping.
C)the SRMC curve is upward- sloping.
D)the SRAC curve is upward- sloping.

Question 5

A feasible input bundle lies:

A)above or on the isoquant of a specified output level.
B)below or on an isoquant of a specified output level.
C)only on the isoquant of a specified output level.
D)below the isoquant of a specified output level.

Question 6

Long run total costs are always:

A)a function of inflation.
B)greater than or equal to short run total costs.
C)equal to short run total costs.
D)less than or equal to short run total costs.

Question 7

Holding output constant, the MRTS is:

A)the ratio of the total products of two inputs.
B)the ratio of the prices of two inputs.
C)the ratio of the APs of two inputs.
D)the ratio of the MPs of two inputs.

Question 8

When returns to scale are decreasing, long run marginal cost is:

A)less than long run average cost.
B)negative.
C)equal to long run average cost.
D)greater than long run average cost.

Question 9

The scale- elasticity of output measures:

A)the slope of the production function.
B)the responsiveness of factor supply to a change in factor price.
C)responsiveness of output to a change in the scale of production.
D)the degree to which inputs can be substituted as output changes.

Question 10

The Marginal Rate of Technical Substitution refers to:

A)the rate of exchange between inputs, holding output constant.
B)the process of developing technical innovations.
C)the rate of exchange between goods, holding utility constant.
D)the process of adopting technical innovations.

Question 11

An isocost line is defined as the set of input bundles that:

A)can be produced at some specified cost.
B)generate one particular level of output.
C)produce the profit- maximizing level of output.
D)can be purchased with a specified sum of money.

Question 12

Fixed proportions production functions always have:

A)varying returns to scale.
B)constant returns to scale.
C)increasing returns to scale.
D)decreasing returns to scale.

Question 13

If a firm is producing at minimum cost and experiences a 4% increase in all input prices

A)output will fall by 4%
B)profits will fall by 4%
C)demand for all inputs will fall by 4%
D)total costs increase by 4%

Question 14

The Marginal Rate of Technical Substitution diminishes when:

A)marginal utility diminishes.
B)demand curves slope down.
C)isoquants are convex.
D)isoquants are linear.

Question 15

The cost function, TC(y), shows the:

A)linear pattern of costs for homothetic production functions.
B)relationship between expenditure on inputs and the scale of input use.
C)minimum expenditure for different outputs, at constant input prices.
D)minimum TC for a level of output, as input- prices vary.

Question 16

What the cheapest input bundle for producing 60 units if f(L,K)= min(3L,2K)?

A)(30,30)
B)(20,30)
C)(30,20)
D)(20,20)

Question 17

If a firm is producing at minimum cost using positive amounts of two inputs, an increase in the price of input one will cause

A)a decrease in the marginal rate of technical substitution
B)an increase in the marginal product of input one
C)a decrease in the absolute value of the slope of the isocost
D)a decrease in the marginal product of input one

Question 18

If the price of just one input rises, a cost- maximizing firm that maintains a constant level of output will use less of the higher- priced input:

A)if the substitution effect outweighs the output effect.
B)and all other inputs.
C)if the output effect outweighs the substitution effect.
D)in all cases.

Question 19

If a firm's production function is f(z₁,z₂)= z₁ + z₂, and if the price of z₁ is $10 and the price of z₂ is
$8, then the minimum cost of producing 10 units of output is:

A)$180.
B)$90.
C)$80.
D)$100.

Question 20

Suppose MTRS =MP_L/MP_K=1/3. If we want to reduce K by 6 units and keep output constant, we have to increase L by units.

A)18
B)12
C)6
D)3

Question 21

A normal input is:

A)one that is a complement with other inputs.
B)one that increases in use with an increase in output.
C)one that decreases in use when its price increases.
D)one that increases in use when income increases.

Question 22

An isoquant may be defined as a curve showing all combinations of inputs:

A)among which the firm is indifferent.
B)capable of producing a level of output.
C)which produce a level of output at minimum cost.
D)which incur a fixed level of TC.

Question 23

If the production function is f(z₁,z₂)= min(z₁,z₂)and if the price of z₁ is $20 and the price of z₂ is
$15, then the minimum cost of producing 10 units of output is:

A)$350.
B)$150.
C)$200.
D)$175.

Question 24

Suppose Diane's spa operates with the production function y = (1200z₁z₂)^2/3. Diane's production function exhibits

A)scale production cannot be determined
B)constant returns to scale
C)increasing returns to scale
D)decreasing returns to scale

Question 25

The Marginal Rate of Technical Substitution is the:

A)product of two marginal products.
B)difference between two marginal products.
C)sum of two marginal products.
D)ratio of two marginal products.

Question 26

Interior solutions of the cost minimizing problem, given convex isoquants, are characterized by:

A)diminishing marginal rate of technical substitution.
B)a tangency between an isoquant and an isocost line.
C)a solution on one of the axes.
D)an intersection between an isoquant and an isocost line.

Question 27

When the price of a resource increases, the cost minimizing quantity of that resource:

A)decreases.
B)increases.
C)is constant.
D)does not increase.

Question 28

Which of the following is not true of a homothetic production function?

A)the output- expansion path is quasi- linear.
B)leads to all input demand functions as downward sloping.
C)has all isoquants the same shape.
D)has all inputs as normal.

Question 29

If a production function exhibits increasing returns to scale, a 10% increase in:

A)input- use results in a less than 10% increase.
B)the LMC being above LAC.
C)output requires a more than 10% increase in the input- use.
D)output results in a less than 10% increase in the input- use.

Question 30

If input prices are constant and the quantity of an input decreases with increases in output, that input is said to be:

A)normal.
B)inferior.
C)advanced.
D)obsolete.

Question 31

An isoquant curve is the set of input bundles such that:

A)the total cost is the same.
B)the level of output is the same.
C)the rate of technical substitution is the same.
D)the economies of scale are the same.

Question 32

If a firm's production function is f(z₁,z₂)= z₁ + z₂, it exhibits:

A)decreasing returns to scale.
B)increasing returns to scale.
C)initially increasing, and subsequently decreasing returns to scale.
D)constant returns to scale.

Question 33

The output- expansion path connects the cost- minimizing input- bundles that:

A)are generated as input- prices fall.
B)can produce various levels of output at a constant TC.
C)can produce expanded levels of output.
D)are generated as output is expanded and input- prices are constant.

Question 34

Relative to some specific level of output, a feasible input bundle is:

A)on the isoquant associated with the level of output.
B)below the isoquant.
C)one that is affordable.
D)one that produces at least the specific level of output.

Question 35

A LRAC curve is U- shaped if:

A)input prices fall at low output levels and rise at higher levels.
B)factors of production become more productive as output expands.
C)decreasing returns to scale follow increasing returns to scale.
D)the production function is homothetic.

Question 36

If doubling all inputs less than doubles the level of output, then the production function exhibits what type of returns to scale?

A)variable
B)increasing
C)decreasing
D)constant

Question 37

For the production function f(z₁,z₂)= min(z₁,z₂), z₁ and z₂ are:

A)imperfect complements.
B)perfect complements.
C)imperfect substitutes.
D)inferior inputs.

Question 38

The LRMC curves will have a downward sloping portion if:

A)organizational difficulties increase as the firm expands.
B)increasing returns to scale occur at low levels of output.
C)the good in question is being produced in a decreasing- cost.
D)diminishing returns occur after some output is produced.

Question 39

Scale elasticity refers to changes in:

A)output due to changes in cost.
B)cost due to changes in output.
C)output due to changes in scale.
D)cost due to changes in scale.

Question 40

Suppose Tariq's body shop operates with the production function y = (1200z₁z₂)^1/2. Tariq's production function exhibits

A)decreasing returns to scale
B)scale production cannot be determined
C)increasing returns to scale
D)constant returns to scale

Question 41

If a firm's production process fits the standard stylization, as its scale increases, its marginal and average output:

A)increase, then decrease, then are constant.
B)decrease, then are constant, then increase.
C)are constant, then increase, then decrease.
D)increase, then are constant, then decrease.

Question 42

Competitive firms are most likely to exist when average cost curves:

A)are U- shaped and achieve their minimum at relatively small output.
B)are horizontal.
C)are U- shaped and achieve their minimum at relatively large output.
D)are upward sloping.

Question 43

When there are many inputs, a firm should employ them so that only inputs:

A)whose marginal product per dollar are identical are hired.
B)with the lowest marginal cost are hired.
C)with the highest marginal product are hired.
D)whose marginal cost is less than their marginal product are hired.

Question 44

Which of the following statements is true?

A)SRTC exceeds LRTC.
B)For any specified output level, LRAC never exceeds SRAC.
C)SRAC exceeds LRTC.
D)SRMC exceeds LRMC.

Question 45

The first principle of cost minimization is:

A)that the optimal input bundle is below the feasible set.
B)that the optimal input bundle is on the isoquant.
C)that the firm maximizes profits.
D)that the optimal input bundle is in the feasible set.

Question 46

A homothetic production function:

A)has constant returns to scale.
B)implies linear marginal cost curves.
C)does not necessarily have isoquants that are the same shape.
D)has linear expansion paths.

Question 47

Figure 7A

The optimum combination of inputs in Figure 7A is given by:

A)points A and C.
B)points F and G.
C)points E and H.
D)points C and D.

Question 48

If the MRTS is constant:

A)the inputs are perfect substitutes.
B)we are dealing with a fixed- proportions production function.
C)the inputs are perfect complements.
D)the production function exhibits constant returns to scale.

Question 49

If a firm's production function is f(z₁,z₂)= z₁ + z₂, its minimum cost of producing y units of output is:

A)y min(w₁,w₂).
B)y(w₁ + w₂)/2.
C)y(w₁ + w₂).
D)yw₁ if w₁ < w₂.

Question 50

If isoquants are smooth and convex, then a necessary condition for cost minimization is that the:

A)cost minimizing bundle intersects the isoquant.
B)MP per dollar of an input equals the MP per dollar of all others.
C)MRTS equals the slope of the isoquant.
D)price of the final good is equal to the MC of production.

Question 51

When returns to scale are increasing, long run marginal cost is:

A)equal to long run average cost.
B)greater than long run average cost.
C)at its minimum.
D)less than long run average cost.

Question 52

Suppose Kate's bakery operates with the production function y = (1200z₁z₂)^1/3. Kate's production function exhibits

A)increasing returns to scale
B)decreasing returns to scale
C)scale production cannot be determined
D)constant returns to scale

Question 53

Suppose that Company X has a production function 3x+y. If the factor prices are 9 for x and 4 for y, how much will it cost to produce 50 units of output?

A)200
B)875
C)1,550
D)150

Question 54

Long run and short run total cost functions are:

A)unrelated to each other.
B)tangent at one point.
C)different names for the same thing.
D)tangent at minimum short run average cost.

Question 55

When returns to scale are constant, long run marginal cost is:

A)horizontal.
B)greater than long run average cost.
C)less than long run average cost.
D)equal to long run average cost.

Question 56

An isoquant represents combinations of:

A)goods with the same utility.
B)inputs with the same cost.
C)goods with the same cost.
D)inputs with the same output.

Question 57

When the minimum wage rises in a competitive labour market, the number of jobs available to workers qualified for such jobs:

A)is constant.
B)does not increase.
C)decreases.
D)increases.

Question 58

When long run average costs reach their minimum, they:

A)are less than long run marginal cost.
B)also minimize the long run marginal cost.
C)are equal to long run marginal cost.
D)are greater than long run marginal cost.

Question 59

If MPL/w_L > MPK/w_K, then the firm should produce using:

A)less L and less K.
B)less L and more K.
C)more L and more K.
D)more L and less K.

Question 60

In the long run a firm will attempt to

A)minimize average variable costs
B)maximize profits subject to an output constraint
C)minimize total costs subject to an input constraint
D)minimize total costs subject to an output constraint

Question 61

Coal- fired steam locomotives become more efficient for railroads relative to oil- burning diesel locomotives as:

A)the price of oil increases.
B)the price of coal increases.
C)railroad freight rates increase.
D)coal- fired steam locomotives become larger.

Question 62

If a firm's production function is f(z₁,z₂)= z₁ + z₂, z₁ and z₂ are:

A)perfect substitutes.
B)perfect complements.
C)inferior inputs.
D)additive inputs.

Question 63

If a firm's cost functions fit the standard stylization, as its output increases its marginal and average costs:

A)decrease, then are constant, then increase.
B)are constant, then increase, then decrease.
C)increase, then decrease, then are constant.
D)increase, then are constant, then decrease.

Question 64

Figure 7A

The optimum quantity of output in Figure 7A is given by the line:

A)ACF.
B)ACB.
C)ADB.
D)ECH.

Question 65

Cost minimization requires:

A)that firms produce above the production function.
B)that the marginal product is equal to unity.
C)that the marginal cost be equal across all inputs.
D)that firms set the MRTS equal to the relative wage.

Question 66

One reason why supply curves slope upward to the right is because:

A)higher prices attract resources from other uses.
B)most goods are necessities.
C)otherwise they would not intersect demand curves.
D)marginal cost is less than elasticity of demand.

Question 67

A firm is currently producing 200 units of output using 60 hours of labour and 80 hours of capital. The marginal product of labour is 12 units of output per hour, and the marginal product of capital is 15 units of output per hour. If the wage rate is $6 per hour and the rental rate of capital is $3 per hour, then:

A)the firm should use more capital and less labour.
B)the firm should use more labour and less capital.
C)we cannot determine if the firm's use of inputs is efficient without more information.
D)the firm's use of labour and capital is cost- efficient.

Question 68

A manufacturing firm uses only capital (K)and labour (L)to produce its product, using a production function of Q = 10KL. It pays its workers w = $15 per hour and has a rental cost of capital of r = $5 per hour. If the firm wants to produce 480 units of output, the optimal bundle of inputs is:

A)(3, 16).
B)(4, 12).
C)(12, 4)
D)(6, 8).

Question 69

What is the marginal rate of technical substitution for the production function y = (1200z₁z₂)^1/2 when Z₂=200 and z₁=100?

A)200
B)2
C)100
D)1

Question 70

In the cost minimization problem, output:

A)and prices are exogenous while the quantity of inputs are endogenous.
B)is exogenous while input quantities and prices are endogenous.
C)is endogenous while input quantities and prices are exogenous.
D)and the quantity of inputs are exogenous while prices are endogenous.

Question 71

The marginal rate of technical substitution is the absolute value of the slope of

A)an isocost
B)a production possibility curve
C)an isoquant
D)an indifference curve

Question 72

Two fuels suitable for heating a building are:

A)perfect complements.
B)imperfect complements.
C)imperfect substitutes.
D)perfect substitutes.

Question 73

An input is said to be an inferior input if:

A)the quantity demanded falls as output rises.
B)MP falls as more of the input is employed.
C)output falls as more of the input is employed.
D)the quantity demanded rises as its price rises.

Question 74

Which of the following is an example of increasing returns to scale?

A)large oil tankers
B)declining average costs
C)railroads
D)metallurgic companies.

Question 75

A change in the relative price of an input in the cost minimization problem:

A)leads to an increase in the use of the cheaper input.
B)leads to less output being produced.
C)leads to more output being produced.
D)leads to higher profits.

Question 76

If a firm's production function is f(z₁,z₂)= z₁ + z₂, its minimum cost of producing y units of output is:

A)y min(w₁,w₂).
B)y(w₁ + w₂).
C)y(w₁ + w₂)/2.
D)yw₁, if w₁ < w₂.

Question 77

If a production function is homothetic, the MRTS:

A)changes unpredictably along a ray from the origin.
B)is constant along a ray from the origin.
C)decreases along a ray from the origin.
D)increases along a ray from the origin.

Question 78

The production function f(z₁,z₂)= min(z₁,z₂)exhibits:

A)constant returns to scale.
B)initially increasing, and subsequently decreasing returns to scale.
C)increasing returns to scale.
D)decreasing returns to scale.

Question 79

For homothetic production functions, the scale factor determines the:

A)scale of production along the output expansion path.
B)total weight of goods produced per period.
C)cost minimizing quantity of output.
D)profit maximizing quantity of output.

Question 80

Figure 7A

Point B in Figure 7A is:

A)infeasible and not optimal.
B)feasible but not optimal.
C)optimal but not feasible.
D)optimal but marginal.