Economics 203: Intermediate Microeconomics I Lab Exercise #1

October 7, 2014

Economics 203: Intermediate Microeconomics I

Lab Exercise #1

Applied Questions

Question 1) Suppose Sandy gets the same utility from each of the 6 combinations of goods Z

and W shown below. Good Z costs $10 per unit and good W costs $4 per unit.

Commodity Combination

1 2 3 4 5 6

Amount of good W

(units)

1

2

4

7

11

16

Amount of good Z

(units)

10

9

8

7

6

5

a) What is the minimum income she musts have to achieve the level of utility

associated with these commodity combinations?

b) If she has the income you found in part a, draw her budget line.

c) Draw her indifference curve.

Question 2: Suppose total income to spend on two products is $100. The price of the

first product is Px=$2 per unit and the price of the second product is Py=$4 per unit.

A) Determine the formula for the budget constraint.

B) What is the MRSy,x?

C) Illustrate the consumption decision with a diagram. (You will not be able to show

the exact consumption bundle.) Make sure you include the intercepts of the

budget constraint and an indifference curve. (2 Marks)

Solutions: Question 1) Suppose Sandy gets the same utility from each of the 6 combinations of goods Z

and W shown below. Good Z costs $10 per unit and good W costs $4 per unit.

Commodity Combination

1 2 3 4 5 6

Amount of good W

(units)

1

2

4

7

11

16

Amount of good Z

(units)

10

9

8

7

6

5

Total income 104 98 96 98 104 114

a) What is the minimum income she musts have to achieve the level of utility associated

with these commodity combinations?

Minimum income must be $96

b) If she has the income you found in part a, draw her budget line.

0 5 10 15 20 25

Good W (units)

c) Draw her indifference curve.

Z

10

5

0

Indifference Curve

Budget line

Question 2: Suppose total income to spend on two products is $100. The price of the

first product is Px=$2 per unit and the price of the second product is Py=$4 per unit. )

a) Determine the formula for the budget constraint.

100

100

4

2

4

25 05

P X P Y

Y X

Y X

x y

.

b) What is the MRSy,x?

MRSP

Py x

x

y

, . 2

405

c) Illustrate the consumption decision with a diagram. (You will not be able to show

the exact consumption bundle.) Make sure you include the intercepts of the

budget constraint and an indifference curve. (2 Marks)

The consumer will consume where MRSP

P

Y

Xy x

x

y

,

Quantity of Y

25

I

0 Quantity of X

50

MRSyx=

Y

X

October 14, 2014


Lab Exercise #2

True or False?

1) A commodity’s income elasticity of demand may be positive or negative.

2) The income elasticity of demand for food is very high.

Section 2: Discussion

Suppose that each of the four corners of an intersection contains a gas station, and that

the gasoline is essentially the same. Do you think that the price elasticity of demand for

each station’s gasoline is above or below 1? Why?

Section 3: Applications:

1) The price elasticity of demand for a particular kind of screwdriver is 2, and the

marginal revenue is $2. What is the price of this screwdriver?

2) The Drink-It Distributors concludes that the demand function for its product

is:

Q=95-73P+82PR+ 0.25 M

where Q is the quantity demanded of its product, P is the price of its product, PR is

the price of its rival’s product, and M is per capita disposable income (in dollars).

Currently, P=$255, PR=$225 and M=$50,650.

a) What is the price elasticity of demand for the firm’s product? Use price elasticity

of demand formula for a point:

Q

P

P

Q

b) What is the income elasticity of demand for the firm’s product?

(Use income elasticity of demand formula for a point:

Q

M

M

Q

.)

c) What is the cross elasticity of demand between its product and its rival’s product.

(Use Cross elasticity of demand formula for a point:

Q

P

P

QR

R

.)

3) According to the U.S. Department of Agriculture, the income elasticity of demand for

coffee is about 0.23. If income rose by 1 percent, what effect would this have on the

quantity demanded of coffee?

4) Give the sign of the cross elasticity of demand for each of the following pairs of

commodities: a) tea and coffee

b) tennis rackets and tennis balls

c) whiskey and gin

Solutions:

Section 1

True or False?

1) A commodity’s income elasticity of demand may be positive or negative. TRUE

2) The income elasticity of demand for food is very high. FALSE

Section 2: discussion

Suppose that each of the four corners of an intersection contains a gas station, and that

the gasoline is essentially the same. Do you think that the price elasticity of demand for

each station’s gasoline is above or below 1? Why?

Elasticity is above 1 because the gasoline provided by the four gas stations are very close

substitutes. Very price sensitive.

Section 3: Applications

1) The price elasticity of demand for a particular kind of screwdriver is 2, and the

marginal revenue is $2. What is the price of this screwdriver?

Since MR= P(1-[1/η]), it follows that P=MR÷(1-[1/η]).

MR=2

η=2=price elasticity of demand

P=2÷(1-½)=4

2) The Drink-It Distributors concludes that the demand function for its product

is:

Q=95-73P+82PR+ 0.25 M

where Q is the quantity demanded of its product, P is the price of its product, PR is

the price of its rival’s product, and M is per capita disposable income (in dollars).

Currently, P=$255, PR=$225 and M=$50,650.

a) What is the price elasticity of demand for the firm’s product? Use price elasticity

of demand formula for a point:

Q

P

P

Q

Solving for Q=95-73(255)+82(225)+0.25(50,650)

Q=12,592.5

Q

P

P

Q

= -73(255/12592.5) = -1.4783

b) What is the income elasticity of demand for the firm’s product?

(Use income elasticity of demand formula for a point:

Q

M

M

Q

.)

0.25 (50,650/12592.5) =1.00556

c) What is the cross elasticity of demand between its product and its rival’s product.

(Use Cross elasticity of demand formula for a point:

Q

P

P

QR

R

.)

82 (225/12592.5) =1.4652

3) According to the U.S. Department of Agriculture, the income elasticity of demand

for coffee is about 0.23. If income rose by 1 percent, what effect would this have on the

quantity demanded of coffee

ηM=[%ΔQd / %ΔM]=0.23

if %ΔM=0.01

then, 0.01*0.23=0.0023

The effect is 0.23% increase in demand.

4) Give the sign of the cross elasticity of demand for each of the following pairs of

commodities:

a) tea and coffee -POSITIVE

b) tennis rackets and tennis balls --NEGATIVE

c) whiskey and gin--POSITIVE

October 21, 2014


Lab Exercise #3

Section A: Test Your Understanding

True or False?

1) The long run refers to a period when all inputs are variable and none is fixed.

2) The average product of an input is the addition to the total output due to the

addition of the last unit of input used, the quantity of other inputs used being held

constant.

3) The law of diminishing marginal returns is not applicable to cases in which there

is a proportional increase in all inputs.

Section B: Questions

Question 1: Sketch the graph of a "standard " short-run production function, and identify

on it the points where the average product peaks(A), the marginal product peaks(B), the

marginal product reaches zero(C), and the average and marginal product intersect(D).

Question 2: Which of the following production functions exhibits increasing returns to

scale?

A) Q = K1/2

Ll/2

B) Q = Kl/2

L2/3

C) Q = Kl/4

Ll/3

D) Q = K/L

Question 3: A representative isoquant for perfect complements is

A) L-shaped.

B) a straight line.

C) a ray passing through the origin.

D) concave.

E) not necessarily any of the above.

Question 4: The production function for calculators is Q = 12L2

- L3, where Q is in

calculators /day and L is in labour-days /day. Show all your work for the following

question.

Give the equation for the marginal product of labour (MPL), and its value when L = 6

labour-days/day.

Question 5: The production function for gravel is Q = 10L

1/2K

1/2 (where Q is in units, L is in labour-

days, and K is in machine-days). With L on the horizontal axis and K on the vertical axis,

give the formula for the MRTS of the relevant isoquant for any given combination of

inputs (K, L), and give the value of the MRTS when L= 9 labour-days and K = 16

machine-days.

Solutions

Section A: Test Your Understanding

True or False?

1) The long run refers to a period when all inputs are variable and none is fixed.

True

2) The average product of an input is the addition to the total output due to the

addition of the last unit of input used, the quantity of other inputs used being held

constant.

False

3) The law of diminishing marginal returns is not applicable to cases in which there

is a proportional increase in all inputs.

True

Section A:

1. Sketch the graph of a "standard " short-run production function, and identify on it the

points where the average product peaks(A), the marginal product peaks(B), the marginal

product reaches zero(C), and the average and marginal product intersect(D).

Ans: The average product of labour peaks at the output level where the ray from the

origin is tangent to the total product curve, where it equals the marginal product of labour

(at A=D). The marginal product peaks at the output level corresponding to the inflection

point on the total product curve (at B), and the marginal product reaches zero when the

total product peaks (at C).

Question 2: Which of the following production functions exhibits increasing returns to

scale?

A) Q = K1/2

Ll/2

B) Q = Kl/2

L2/3

C) Q = Kl/4

Ll/3

D) Q = K/L

Ans: B

Question 3: A representative isoquant for perfect complements is

A) L-shaped.

B) a straight line.

C) a ray passing through the origin.

D) concave.

E) not necessarily any of the above.

Ans: A

Question 4: The production function for calculators is Q = 12L2

- L3, where Q is in

calculators /day and L is in labour-days /day. Show all your work for the following

questions.

Give the equation for the marginal product of labour (MPL), and its value when L = 6

labour-days/day.

Ans: MPL = 24L - 3L2

, which equals 36 calculators/labour-day when L = 6 labour-

days/day.

Question 5 : The production function for gravel is Q = 10L

1/2K

1/2 (where Q is in units, L is in labour-

days, and K is in machine-days).

With L on the horizontal axis and K on the vertical axis, give the formula for the MRTS

of the relevant isoquant for any given combination of inputs (K, L), and give the value of

the MRTS when L= 9 labour-days and K = 16 machine-days.

MRTSMP

MP

L K

L K

K

L

L

K

5

5

16

9

1 2 1 2

1 2 1 2

/ /

/ /

October 28, 2013


Lab Exercise #4

Section 1: Discussion:

Explain the why the short-run minimum cost of producing a certain output may

differ from the long-run minimum cost. Illustrate your explanation with a diagram.

Section 2: Application:

For the Bridges-to-Shores Corporation, the relationship between output (Q) and

the number of hours of specialized manual labour (S) and machine-

operated labour (M) is:

Q=650S +145M - 0.45 S2 - 0.65M

2

The hourly wage of specialised manual labour is $42, and the hourly wage of

machine-operated labour is $25. The firm can hire as much labour as it wants at

these wage rates.

A) The vice president of manufacturing recommends that the firm hire 50 hours of

manual labour and 95 hours of machine-operated labour. Evaluate this

recommendation.

B) If the Bridges-to-Shores company decides to spend a total of $25,000 on inputs

(specialized manual and machine-operated labour), how many hours of each type of

labour should it hire?


Lab Exercise # 4 Solutions


Explain the why the short-run minimum cost of producing a certain output may

differ from the long-run minimum cost. Illustrate your explanation with a diagram.

In the short-run, at least one factor of production is assumed fixed. When this

happens and the firm must produce a specific quantity of output, the firm may not be

able to use the input combination that attains minimum cost relative to the long-run

situation. In the long run, all factors of production are variable. Hence, a firm will

produce a specific output where the isocost line is tangent to the isoquant (the specific

quantity that must be produced). In the short-run, this may not be possible for a

specific quantity.

Capital

K1

K*

L1 L2

If capital is fixed at K* units, and the firm must produce q1 units, L2 units of labour will

be used with this fixed amount of capital to produce q1 units of output. The total cost is

C2. If the firm were able to use any combination of K and L, it would use L1 and K1

units of labour and capital and lower its cost to C1. This would be the long-run solution.

Total cost is C1.

q1

C0 C1

C2

q0

Expansion Path

q2

Minimum cost input

combination to produce

q1 units.

Actual input combination to

produce q1 units when K is

fixed.

Section 2: Application:

For the Bridges-to-Shores Corporation, the relationship between output (Q) and

the number of hours of specialized manual labour (S) and machine-

operated labour (M) is:

Q=650S +145M - 0.45 S2 - 0.65M

2

The hourly wage of specialised manual labour is $42, and the hourly wage of

machine-operated labour is $25. The firm can hire as much labour as it wants at

these wage rates.

B) The vice president of manufacturing recommends that the firm hire 50 hours of

manual labour and 95 hours of machine-operated labour. Evaluate this

recommendation.

To find the optimal input combinations, choose where:

MP

P

MP

P

S

S

M

M

The marginal products are:

MPS= 650 - 0.9S

MPM =145 – 1.3M

MP

P

MP

P

S Mcross multiply

S M

S M

S M

S M equation

S

S

M

M

650 0 9

42

145 1 3

25

25 650 9 42 145 1 3

16250 22 5 6090 54 6

22 5 10160 54 6

4515556 2 426667

. .

( . ) ( . )

. .

. .

. .

Enter in S=50 and M=95 into either equation we see that this is not the optimal

input combination.

50 4515556 2 42667 95

50 682 08925

. . ( )

.

B) If the Bridges-to-Shores company decides to spend a total of $25,000 on inputs

(specialized manual and machine-operated labour), how many hours of each type of

labour should it hire?

TC=25,000

TC P S P M

25,000 S

25,000

25,000

6034.6648 = 126.92014M

M = 47.5469

S = 451.5556 + 2.42667M = 566.9363

s M

42 25

42 4515556 2 42667 25

189653352 10192014 25

M

M M

M M

( . . )

. .

Must use 567 hours of specialized labour and 47.5 hours of machine-operated labour.


Lab Exercise #5

Section 1: Test Your Understanding

True or False?

1) No industry, now or in the past, has met all of the requirements of perfect competition.

2) Under perfect competition the product of any one seller must be the same as the product

of any other seller.

3) For a perfectly competitive firm, choose the output rate at which marginal cost is equal to

price.

4) If a firm’s marginal cost curve intersects its average variable cost curve at $4 per unit out

output, the firm will shut down in the short run if the price of its product falls below $4

per unit.


1) Suppose that the total costs of a perfectly competitive firm are as follows:

Output Rate Total cost

0 40

1 60

2 90

3 130

4 180

5 240

a) If the price of the product is $50, what output rate should the firm choose?

b) Suppose the firm experienced an increase of $30 in its fixed costs. What is its new total

cost function?

c) What effect will this increase in its fixed costs have on the output it will choose?

d) After the increase in fixed costs, what does the firm’s marginal cost curve look like?

e) After the increase in fixed costs, what output rate would the firm choose if the price of

its product were $40?

2) Data are provided below concerned the Allied Peanut Company, a firm

producing peanut brittle.

A) Supposing that this firm is a member of a perfectly competitive industry, complete the table

below:

Output per

day

Price Total Cost Total

revenue

Profit Marginal

cost

0 200 100

1 200

2 310

3 500

4 700

5 1000

B) Assume that the output rate must equal an integer number per day. If price of peanut

brittle falls to $50, will Allied continue producing, or will it shut down?

C) What is the minimum price at which Allied will continue production?

D) If price is $200, what output rate will Allied choose?

Solutions:

Section 1

1) True

2) True

3) True

4) True


Suppose that the total costs of a perfectly competitive firm are as follows:

Output Rate Total cost

0 40

1 60

2 90

3 130

4 180

5 240

a) If the price of the product is $50, what output rate should the firm choose?

Produce where P=MC

Output Rate Total cost Marginal cost

0 40

20

1 60

30

2 90

40

3 130

50

4 180

60

5 240

Should produce 3 or 4 units.

b) Suppose the firm experienced an increase of $30 in its fixed costs. What is its

new total cost function?

Output Rate Total cost +30 =New TC

0 40+30=70

1 60+30=90

2 90+30=120

3 130+30=160

4 180+30=210

5 240+30=270

c) What effect will this increase in its fixed costs have on the output it will choose?

None.

Output Rate Total cost +30 =New TC MC new

0 40+30=70

20

1 60+30=90

30

2 90+30=120

40

3 130+30=160

50

4 180+30=210

60

5 240+30=270

d) After the increase in fixed costs, what does the firm’s marginal cost curve look

like? As above. Same as before the increase in fixed cost.

e) After the increase in fixed costs, what output rate would the firm choose if the

price of its product were $40? 2 to 3 units.

Lab Exercise #7

Price Discrimination


Some university bookstores give faculty a discount that students do not receive. Show

with a sketch graph why this practice is most likely a profit-maximizing strategy instead

of a college perk given to the faculty at college expense.


1. The demand curve facing a monopolist is given by P = 350 – 7Q, and the short-run

total cost curve is given by TC = 500 + 70Q, where TC is in $s and Q is in tonnes.

What are the profit-maximizing price and quantity? Find the monopolist's economic

profit.

2. A monopolist faces two separate demand curves: P1 = 65 – 2 Q1 and P2 = 35 – 3 Q2.

The total cost curve is TC = 7 + 5Q. Find, P1, P2, Q1,and Q2.

3. Find the price elasticities of demand at equilibrium for Problem 2.

Solutions:


Some university bookstores give faculty a discount that students do not receive. Show

with a sketch graph why this practice is most likely a profit-maximizing strategy instead

of a college perk given to the faculty at college expense.

Ans:

PricePrice Price

Quantity

Studentmarket

Ps

MR D

Faculty market

MR

D

PfHorizontal sum of

both markets

MC

GMR

The graph shows a situation where the student demand is more inelastic at any price level

than the faculty demand. (At any given price the location on the demand curve is

proportionately further down the demand curve for the students.) For this reason, they

can be charged a higher price. By observing where the MC is equal to the marginal

revenue received from both markets, the bookstore manager will discover that overall

profits are maximized when he charges Ps to the students and Pf to the faculty.

Section 2: Applications: 1. The demand curve facing a monopolist is given by P = 350 – 7Q, and the short-run

total cost curve is given by TC = 500 + 70Q, where TC is in $s and Q is in tonnes.

What are the profit-maximizing price and quantity? Find the monopolist's economic

profit.

Marginal cost is equal to the slope of the straight line total cost curve:

MC = 70.

Marginal revenue has a slope which is twice as large as the slope of the demand curve:

MR = 350 – 14Q.

Set MC = 70 = 350 – 14Q = MR:

Q = 280/14 = 20 tonnes.

P = 350 – 7(20) = 350 – 140 = $210/tonne.

Profit = PQ – TC = 210(20) – [500 + 70(20)] = 4200 – 1900 = $2300.

2. A monopolist faces two separate demand curves: P1 = 65 – 2 Q1 and P2 = 35 – 3 Q2.

The total cost curve is TC = 7 + 5Q. Find, P1, P2, Q1,and Q2.

MC = slope of TC = 5

MR1 = 65 – 4 Q1

MR2 = 35 – 6 Q2

Set MR1 = MR2 = MC.

First solve for Q1 and P1:

65 – 4 Q1 = 5

4 Q1 = 60

Q1 = 60/4 = 15 kg.

P1 = 65 – 2(15) = $35/kg.

Next solve for Q2 and P2:

35 – 6 Q2 = 5

6 Q2 = 30

Q2 =30/6 = 5 kg.

P2 = 35 – 3(5) = $20/kg.

3. Find the price elasticities of demand at equilibrium for Problem 2.

Elasticity l = (∆Q1/∆P1)(P1/Q1) = (–1/2)(35/15) = –7/6.

Elasticity 2 = (–1/3)(20/5) = –4/3.

Check:

MR= P(1 + 1/)

MR1 = 35(1 – 6/7) = 5

MR2 = 20(1 – 3/4) = 5


Lab Exercise #8

Section 1: Test Your Understanding

The following payoff matrix represents the long-run payoffs for two duopolists faced

with the option of buying or leasing buildings to use for production. Determine whether

any dominant strategies exist and whether or not there is a Nash equilibrium.

Firm 1

Lease

Building

Buy

Building

Lease F1 = 500 F1 = 750

Firm 2 F2 = 500 F2 = 400

Buy F1 = 300 F1 = 600

F2 = 600 F2 = 200


What are the fundamental differences among the Cournot, Bertrand, and Stackelberg

models of oligopoly?

Section 3: Application

The market demand curve for a pair of Cournot duopolists is given as P=36-3Q,

where Q=Q1+Q2. For each duopolists, the constant per unit marginal cost is $18/unit

and fixed costs are zero.

a) Find the Cournot equilibrium price, quantity and profits.

b) Solve the problem for Bertrand duopolists.

c) Find the equilibrium price, quantity and profit for each firm, assuming the

firms act as a Stackelberg leader and follower, with Firm 1 as the leader.

Solutions:

Section 1

The following payoff matrix represents the long-run payoffs for two duopolists faced

with the option of buying or leasing buildings to use for production. Determine whether

any dominant strategies exist and whether or not there is a Nash equilibrium.

Firm 1

Lease

Building

Buy

Building

Lease F1 = 500 F1 = 750

Firm

2

F2 = 500 F2 = 400

Buy F1 = 300 F1 = 600

F2 = 600 F2 = 200

The dominant strategy for firm 1 is to buy the building, since regardless of firm 2’s

strategy, firm 1 is better off buying the building. Firm 2, on the other hand, is better off

buying the building only if firm 1 leases; since firm 1 will not lease, firm 2 should lease.

Nash equilibrium occurs when firm 1 buys and firm 2 leases, since this is the best

strategy for each player given the strategy chosen by the other player.

Section 2: Discussion: What are the fundamental differences among the Cournot,

Bertrand, and Stackelberg models of oligopoly?

The models differ in their assumptions about firm behaviour.

The Cournot model assumes that firms choose quantities simultaneously (taking as

given the other firm’s quantity).

The Bertrand model assumes that firms choose prices simultaneously (taking as given the

other firm’s price.)

The Stackelberg model assumes that one firm (the leader) chooses its quantity before the

other firm (the follower) chooses its quantity, and that the leader takes into account how

the follower will respond to the leader’s quantity decision.


a) P1 = 36 – 3Q = 36 – 3 (Q1 + Q2 ) = (36 – 3 Q2 ) – 3 Q1.

MR1 = (36 – 3Q2) – 6Q1 = MC = 18.

1’s reaction function: Q1 = 3 – (1/2) Q2.

Similarly for 2: Q2 = 3 – (1/2) Q1.

This solves for Q1 = Q2 = 2 units.

P = 36 – 3Q = 36 – 3(4) = $24/unit.

1 = TR – TC = 2(24) – 2(18) = $12 = 2.

= 1 + 2 = $24.

b) P = MC = $18/unit.

Since P = 36 – 3Q, we have Q = 6.

Thus, Q1 = Q2 = Q/2 = 3 units.

TR1 = TR2 = 3(18) = $54.

TC1 = TC2 = 3(18) = $54.

So 1 = 2 = = $0.

c) 2’s reaction function is the same as in the Cournot case: Q2 = 3 – (1/2)Q1.

1’s demand is

P = 36 – 3(Q2) – 3Q1 = 36 – 3(3– (1/2)Q1) – 3Q1 = 27 – (3/2) Q1.

MR1 = 27 – 3Q1 = MC = $18/unit.

This solves for Q1 = 3 units and Q2 = 1.5 units.

Therefore Q = Q1 + Q2 = 4.50 units and P = 36 – 3(4.5) = $4.50/unit.

1 = 3 (45/2 – 18) = $13.50.

2 = (3/2) (45/2 – 18) = $6.75.

:

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Economics 203: Intermediate Microeconomics I Lab Exercise #1