# EC3000 Advanced Microeconomics – Suppose that a ﬁrm produces some level of output

Question

EC3000 Advanced Microeconomics

Coursework

Instructions: The coursework below contains 10 multiple choice questions. For each question, there are ﬁve potential answers: (a), (b), (c), (d), and (e). Circle the letter(s) corresponding to your answer(s) for each question. (Notice that you can circle multiple letters if

you believe that a question has multiple correct answers.)

Marking: For each question, you will be awarded points for circling correct answers and

for not circling incorrect answers. For example, suppose that (a) is a correct answer: if you

circle (a), then you will be awarded 1 point, and if you do not circle (a), then you will be

awarded 0 points. Similarly, suppose that (b) is an incorrect answer: if you circle (b), then

you will be awarded 0 points, and if you do not circle (b), then you will be awarded 1 point.

For every question that is awarded 5 points in total, you will be awarded 5 additional points.

Deadline: You have one week to complete this coursework. The deadline for handing in at

Reception in the Astley Clarke Building is Thursday, 10 December 2017, at 3.00pm. Late

submissions will not be accepted.

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(1) Suppose that a ﬁrm produces some level of output y ≥ 0 according to the production

function f : R2 → R+ , which is given by

+

y = f (K, L) = K + L,

where K ≥ 0 is capital and L ≥ 0 is labor. Further suppose that r > 0 is the rental rate

for capital and w > 0 is the wage rate for labor, and that the ﬁrm wants to minimize

its costs in order to produce some level of output y. Which of the following statements

are false? Circle all that apply.

(a) The conditional factor demand for capital is always positive.

(b) The conditional factor demand for labor is always positive.

(c) The conditional factor demand for capital is never positive.

(d) The conditional factor demand for labor is never positive.

(e) The conditional factor demand for capital is always equal to the conditional factor

demand for labor.

(2) Suppose that a consumer has a preference ordering over R+ that is represented by

the utility function u : R+ → R, which is given according to

u(x1 , x2 , . . . , x ) =

ui (xi ).

i=1

Which of the following statements are true? Circle all that apply.

(a) The marginal rate of substitution between any two goods is independent of the

consumption of those same two goods.

(b) The marginal rate of substitution between any two goods is not independent of

the consumption of those same two goods.

(c) The marginal rate of substitution between any two goods is independent of the

consumption of any other goods.

(d) The marginal rate of substitution between any two goods is not independent of

the consumption of any other goods.

(e) The marginal rate of substitution between any two goods is necessarily equal to

the marginal rate of substitution between any two other goods.

(3) Suppose that a consumer has a preference relation

on R+ that is complete and

transitive. When does there exist a utility representation of ? Circle all that apply.

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(a) A representation exists if

is continuous and locally nonsatiated.

(b) A representation exists if

is continuous and strictly monotonic.

(c) A representation exists if

is continuous and strictly convex.

(d) A representation exists if

is continuous, locally nonsatiated, and strictly convex.

(e) A representation exists if

is continuous, strictly monotonic, and strictly convex.

(4) Consider a ﬁrm that requires more than one costly inputs to produce a single output.

Suppose that the ﬁrm’s production function is continuous, strictly increasing, and

strictly quasiconcave, and also exhibits constant returns to scale (CRS). Which of the

following statements are true for a cost-minimizing ﬁrm? Circle all that apply.

(a) The ﬁrm’s costs are strictly increasing in output.

(b) The ﬁrm’s costs are constant per unit of output.

(c) The ﬁrm’s marginal costs are strictly increasing in output.

(d) The ﬁrm’s marginal costs are constant at every level of output.

(e) The ﬁrm’s marginal costs are zero.

(5) Suppose that a preference relation on R+ is complete and transitive. Let and ∼

denote the strict and indiﬀerence relations on R+ , respectively, which can be derived

from . Which of the following statements are false? Circle all that apply.

(a) The strict relation

is complete.

(b) The indiﬀerence relation ∼ is complete.

(c) The strict relation

is transitive.

(d) The indiﬀerence relation ∼ is transitive.

(e) The strict relation

and the indiﬀerence relation ∼ are complete and transitive.

(6) Suppose that a consumer has a lexicographic preference ordering over R2 , i.e., for

+

any x, y ∈ R2 , x

y if x1 > y1 , or if x1 = y1 and x2 ≥ y2 . Which of the following

+

statements are true? Circle all that apply.

(a) The preference is complete and transitive.

(b) The preference is complete, transitive, and continuous.

(c) The preference is complete, transitive, and locally nonsatiated.

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(d) The preference is complete, transitive, continuous, and locally nonsatiated.

(e) The preference is neither complete nor transitive.

(7) Suppose that a consumer has a preference relation

statements are true? Circle all that apply.

over R+ . Which of the following

(a) The preference relation is strictly monotonic if it is locally nonsatiated.

(b) The preference relation is locally nonsatiated if it is strictly monotonic.

(c) The preference relation is strictly monotonic if it is strictly convex.

(d) The preference relation is strictly convex if it is strictly monotonic.

(e) The preference relation is locally nonsatiated if it is strictly convex.

0, and has

(8) Suppose that a consumer must choose from R2 , faces prices p = (p1 , p2 )

+

2

income w > 0. Her indirect utility function v : R++ × R++ → R is given according to

v(p1 , p2 , w) =

1

4p1

3

4p2

w4 .

Which of the following statements are false? Circle all that apply.

(a) The demand for good 1 is more income elastic than the demand for good 2.

(b) The demand for good 2 is more income inelastic than the demand for good 1.

(c) The demand for good 2 is more income elastic than the demand for good 1.

(d) The demand for good 1 is more income inelastic than the demand for good 2.

(e) The income elasticity of demand for good 1 is always equal to the income elasticity

of demand for good 2.

(9) Suppose that a consumer has a preference ordering over R+ that can be represented

by a utility function u : R+ → R. Further suppose that the consumer faces prices

p = (p1 , p2 , . . . , p )

0 and has income w > 0. Which of the following statements are

true? Circle all that apply.

(a) If u is locally nonsatiated, then the consumer exhausts her budget.

(b) If u is strictly increasing, then the consumer exhausts her budget.

(c) If u is quasiconcave, then the consumer exhausts her budget.

(d) If u is strictly quasiconcave, then the consumer exhausts her budget.

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(e) If u is strictly quasiconvex, then the consumer exhausts her budget.

(10) Suppose that a ﬁrm produces some level of output y ≥ 0 according to the production

function f : R2 → R+ , which is given by

+

√

√

y = f (K, L) = ( K + L)2 ,

where K ≥ 0 is capital and L ≥ 0 is labor. Further suppose that r = 10 is the rental

rate for capital and w = 5 is the wage rate for labor, and that the ﬁrm is perfectly

competitive. Which of the following statements are true? Circle all that apply.

(a) The market output price is less than one.

(b) The market output price is greater than two.

(c) The market output price is less than three.

(d) The market output price is greater than four.

(e) The market output price is less than ﬁve.