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FEEDBACK TUTORIAL LETTER

1st SEMESTER 2017

ASSIGNMENT 1

INTERMEDIATE MICRO-ECONOMICS

IMI611S

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Solutions and explanations to the questions are provided in italics

Question One [30 marks]

The current world production of oil is 100 million barrels per day and the current

world price of oil is $40 per barrel. The price elasticity of demand (ε) is -0.5 and the

elasticity of supply (η) is 0.4. Kati Investment is planning to enter the world oil

market with a daily production of 0.9 million barrels of oil per day. For simplicity,

assume that the supply and demand curves are linear.

a) Use a well labelled diagram to analyze the effect of Kati Investment production on

the world price and quantity. [5 marks]

This question asks what is the effect of Kati Investment production on the world

market for oil. What we know is that the current equilibrium quantity is 100

million barrels and the current equilibrium price $40 per barrel. If Kati

Investment comes into the market, it will increase market supply by 0.9 million

barrels per day. Thus we can analyse the effect of Kati Investments through a

shift in the supply curve: an increase in supply will result in the supply curve

shifting to the right. This is reflected in the graph below:

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Please take note: A graph only means something if it is labelled fully. Thus you

need to fully label your graphs to show understanding (and to get any marks). You

must always fully label graphs, including:

The axes (i.e. price and quantity)

The curves (i.e. the demand and supply curve)

The points of the graphs (i.e. e1 with P1 and Q1 and e2 with P2 and Q2).

In addition to labelling graphs, if the question involves a shift in either the

demand or supply curve, you need to show the shift. You do this by labelling the

new supply curve differently (e.g. S2, whereas the first supply curve was labelled

S11) and showing the direction of the shift with an arrow. You should also show

the new equilibrium price and quantity by labelling the new points as P2 and Q2

respectively and showing the direction of the shift in price and quantity with

arrows.

Beyond presenting the graph, the question asks you to analyse the effect on the

increase in supply due to Kati Investment entering the market on the world

prices. Thus in addition to drawing the graphs, you need to provide an

explanation of the shift.

Tip: Get into the practice of labelling graphs fully and providing explanations of

the shift. When it comes to exam time, presenting a graph fully labelled should

come naturally to you.

Explanation of the shift: When the new firm enters the oil market, the total

supply will increase which will cause the supply curve to shift to the right. An

increase in supply will result in a decrease in the equilibrium price from P1 (40)

to P2, and an increase in the equilibrium quantity from Q1 (100) to Q2.

b) Use the information provided above to determine the long-run demand and supply

functions that are consistent with pre-Kati Investment world output and price.

[10 marks]

You need to make use of the information provided to determine the demand and

supply functions. The general demand function form is Qd = a - bP, so we need to

find a and b (note the negative relationship between Q and P for the demand

function, shown as –b). We have been told that the price elasticity of demand (ε)

is -0.5. We also know that b = the slope of the demand curve is = ∆ P / ∆Q, and

(ε) = (P/Q)( ∆ P / ∆Q). 1 You could also use S0 and S1 annotations

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So, ∆ P / ∆Q = 0.5 (Q/P) = 0.5 (100/40) = 1.25

Then, solve for a by plugging in values for P & Q:

Let P = 40, Q =100

Qd= a -1.25P

100 = a – 1.25(40)

100 = a -50

a = 150

So the demand function, Qd = a – bP

Qd = 150 -1.25 P

The general supply function form is Qs = c + dP, so we need to find c and d (note

the positive relationship between Q and P for the supply function, shown as +d).

We have been told that the elasticity of supply (η) is 0.4. We also know that c =

the slope of the supply curve is = ∆ P / ∆Q, and (η) = (P/Q)( ∆ P / ∆Q).

So, ∆ P / ∆Q = 0.4 (Q/P) = 0.4 (100/40) = 1

Then, solve for c by plugging in values for P & Q:

Let P = 40, Q =100

Qs= c + 1P

100 =c + 1(40)

100 = c + 40

C = 100 – 40 = 60

So the supply function, Qs = c + dP

Qs = 60+ P

c) Determine the post-Kati Investment long-run linear supply function

[5 marks]

The ‘post-Kati Investment’ supply function is the supply function after Kati

Investment has entered the market. Thus we need to take into account Kati

Investment’s supply into the total market supply. We do this simply by adding

Kati Investment’s to the market supply. So:

Qs = 60 + P +0.9

Qs =60.9+P

As simple as that!

d) Use the demand function and the post-Kati Investment supply function to calculate

new equilibrium price and quantity.

[5 marks]

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Here, you needed to be careful in reading the question and determining what

was being asked. Some students solved for the Pe (equilibrium price) & Qe

(equilibrium quantity) with the supply function before Kati Investment (i.e. Qs =

60 + P), however this gave you Pe = 40 and Qe = 100, which are the figures that

were provided to you! What the question was asking for was the new Qe and Pe.

To solve for Qe and Pe, equate the Qd and the Qs (post- Kati Investment).

So: Qd = 150 -1.25 P = Qs + 60.9 +P

150 – 60.9 = 2.25P

2.25 P = 89.1

So new Pe = N$ 39.60

Find new Qe: Qd = 150 - 1.25P

Qe = 150 – 1.25(39.6) = 100.5

So new Qe = 100.5

Please take note: You needed to show your workings in terms of how you got Qe

and Pe. You would have lost marks even if you had the right answers but you did

not show your workings. In general, always show your workings, first to

demonstrate to the marker that you understand the question, and secondly if

you go wrong, you may get part-marks from your workings.

e) Explain why the equilibrium quantity increases with less than 0.9 million. [5

marks]

Note that when Kati Investment entered the market, there was an increase in

market supply by 0.9 million barrels, however the equilibrium quantity increased

by 100.5 – 100 = 0.5 million (so less than the supply increase). This is because

when the quantity supplied increased with Kati Investment entering the market,

the equilibrium price decreased (this effect is covered in (a)). In response to the

decrease in the equilibrium price, existing firms in the market reduced their

supply (by 0.4 million). Thus due to the suppliers price elasticity of supply - the

equilibrium quantity did not increase one for one with the increase in quantity

supplied.

Question Two [25 marks]

a) People makes trade-offs because they can’t have everything. State three trade-

offs a society faces. [3 marks]

The trade-offs society faces due to the scarcity of resources are:

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Which goods and services to produce – If society chooses to focus production

on one type of good or service, it must produce fewer other goods and

services due to the scarcity of resources.

How to produce – To produce a given level of output, a firm must use more of

one input if it uses less of another input.

Who gets the goods or services – The more of society’s goods and services one

individual / group gets the less another individual / group gets.

Please take note: Trade-off means giving up something to get something else. In

economics, we consider the trade-offs in resource allocation and distribution as

it helps us think about how economic decisions impact on society. For example, if

the government decides to spend its entire budget on national defence, there is

no budget available for infrastructure development or social grants.

a) The demand function for roses is 𝑄 = 200 − 0.4𝑝, and the supply function is

𝑄 = 100 + 0.4𝑝 + 0.5𝑡, where p is the price of roses and t is the average

temperature in a month. Show how the equilibrium price varies with temperature.

[5 marks]

In order to show how the equilibrium price varies with the temperature, we need

to find the relationship between the equilibrium price and the temperature. So

we should solve for Pe.

Qd = 200 – 0.4 p = Qs = 100 + 0.4 p + 0.5 t

200 – 100 = 0.4 p + 0.4 p + 0.5t

0.8 p + 0.5 t = 100

Make Pe the subject of the formula:

0.8 p = 100 – 0.5 t

Pe = 125 – 0.625t

So now that we have a formula that expresses Pe in terms of temperature, we

can determine the relationship: There is a negative relationship between Pe and

temperature, indicated by the negative sign relating the two variables.

The question asked for us to show how the equilibrium price varies with

temperature, so we need to directly answer what the question asks: The

equilibrium price varies negatively with the temperature. E.g. If temperature

increases, Pe will decrease.

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Please take note: You could have shown the negative relationship in another

way. For example, by plugging in different values for t, you could have shown

that Pe decreases as t increases.

Tip: You should be able to tell the relationship (negative or positive) between

variables based on the functional relationship between the variables. For

example:

Qd = a – bP: There is a negative relationship between Qd and P (when P

increases, Qd decreases)

Qs = c + dP: There is a positive relationship between Qs and P (when P

increases, Qs increases).

b) The demand function for processed pork is Q = 100−P + 5Pb + Pc + 8Y and supply

function for processed pork is Q = 50 + P−6Ph where Pb is the price of beef, Pc is

the price of chicken, Ph is the price of hog and Y is the consumer income. Initial

values are Pb=N$2, Pc=N$5, Y=N$100 and Ph=N$3. Draw the demand and supply

curve for processed pork. [8 mark]

In order to draw the demand or supply curves, you need to first determine the

demand and supply functions.

So: Qd = 100 – P + 5Pb + Pc + 8Y

Plug in the values provided:

Qd = 100 – P +5(2) + 5 + 8(100)

Qd = 100 – P + 815

Qd = 915 – P – Demand function for processed pork

Qs = 50 + P−6Ph

Qs = 50 + P – 6(3)

Qs = 32 +P – Supply function for processed pork

You could have also determined the equilibrium price and quantity of processed

pork (although this was not required):

Qd = 915 – P = Qs = 32 +P

883 = 2P

Pe = 441.5

Qe = 915 – 441.5 = 473.5

With the demand and supply functions, you can draw the demand and supply

curves.

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Please take note: A graph only means something if it is labelled fully. Thus you

need to fully label your graphs to show understanding (and to get any marks). You

must always fully label graphs, including:

The axes (i.e. price and quantity)

The curves (i.e. the demand and supply curve)

The points of the graphs (e.g. the points of equilibrium)

c) Use a well labelled diagram to analyse the effect of an increase in the price of

chicken on the equilibrium price and quantity of pork assuming chicken and pork

are substitutes. [4 marks]

Chicken and pork are substitutes, and thus an increase in the price of chicken will

cause customers to substitute pork for chicken. Thus an increase in the price of

chicken will cause an increase in the quantity demanded for pork. This will cause

the demand curve for pork to shift to the right. Let’s show this graphically.

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Beyond presenting the graph, the question asks you to analyse the effect of the

increase in the price of chicken on the equilibrium price and quantity of pork. So

the increase in the price of chicken, which is a substitute, will cause the quantity

demanded of pork to rise. The demand curve for pork will shift to the right from

D1 to D2 in the above graph. Equilibrium quantity will increase from Q1 to Q2 and

equilibrium price will increase from P1 to P2.

Please take note: A graph only means something if it is labelled fully. Thus you

need to fully label your graphs to show understanding (and to get any marks). You

must always fully label graphs, including:

The axes (i.e. price and quantity)

The curves (i.e. the demand and supply curve)

The points of the graphs (i.e. e1 with P1 and Q1 and e2 with P2 and Q2).

d) Suppose that the inverse demand function for music show is 𝑃 = 100 − 0.25𝑄 and

the supply function for music show is Q = 50 + 𝑃. Calculate elasticity of demand at

equilibrium for this music show. [5 marks]

The formula for price elasticity of demand is (Pe / Qe )(Slope of demand curve)

Thus we need to find those three points in order to determine elasticity of

demand.

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First, find the demand function from the inverse demand function given (i.e.

make Qd the subject of the formula).

So: P = 100 – 0.25 Qd

-0.25 Qd = P -100

Qd = -4P + 400

So Qd = 400 – 4P

Thus the slope of the demand curve is -4

Now, lets find Qe and Pe (equilibrium quantity and price)

Qd = Qs

400 – 4P = 50 + P

350 = 5P

Pe = 70

Qe = 50 + 70 = 120

Now we can solve for the price elasticity of demand as:

(ε) = -b (Pe/Qe)

(ε) = -4 (70/120)

(ε) = - 2.33

Please take note: The price elasticity of demand is always negative as there is a

negative relationship between price and quantity demanded.

We can interpret this as: Since (ε) is greater than one, the price elasticity of

demand for the music show is elastic (i.e. a small change in price would result in

a big change in demand).

Question Three [25 marks]

a) Explain the following economics concepts:

- Economies of scale – This is a property of a cost function whereby the average

cost of production falls as output expands. Economies of scale are the cost

advantages that enterprises obtain due to size, output, or scale of operation,

with cost per unit of output generally decreasing with increasing scale as fixed

costs are spread out over more units of output.

- Diseconomies of scale – This is a property of a cost function whereby the

average cost of production rises when output increases. Diseconomies of scale

are an economic concept referring to a situation in which economies of scale

no longer functions for a firm. With this principle, rather than experiencing

continued decreasing costs and increasing output, a firm sees an increase in

marginal costs when output is increased.

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- Economies of scope – A proportionate saving gained by producing two or more

distinct goods, when the cost of doing so is less than that of producing each

separately.

- Production possibility frontier - The production possibility frontier (PPF) is

a curve depicting all maximum output possibilities for two goods, given a set

of inputs consisting of resources and other factors. The PPF assumes that all

inputs are used efficiently.

Tip: You can also use graphs to illustrate theoretical concepts. For example,

the PPF is illustrated below:

Source: Policonomics, 2012

b) The production function for the automotive industry is 𝑄(𝐾, 𝐿) = 2𝐾0.4𝐿0.6, where K

and L are inputs in the production.

i. If you double the inputs, what will happen to the outputs? Show your works.

[5 marks]

You must show what happens to outputs by plugging in 2 K and 2 L into the

production function. So:

Input 2K and 2L: 𝑄(2𝐾, 2𝐿) = 2(2𝐾)0.4(2𝐿)0.6

Raise each of the components in the brackets to the respective powers:

𝑄(2𝐾, 2𝐿) = 2(2)0.4(𝐾)0.4 (2)0.6(𝐿)0.6

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𝑄(2𝐾, 2𝐿) = 2(2)0.4+0.6(𝐾)0.4 (𝐿)0.6

𝑄(2𝐾, 2𝐿) = 2(2)1(𝐾)0.4(𝐿)0.6 Note that 2 to the power of 1 equals 2

𝑄(2𝐾, 2𝐿) = 4𝐾0.4𝐿0.6

So, if we double both inputs (e.g. increase K and L to 2 K and 2 L), we increase Q

from 2𝐾0.4𝐿0.6 to 4𝐾0.4𝐿0.6. Thus if we double inputs, we double outputs.

Please take note: The question asks what happens to output, so you need to

explicitly state that output doubles when inputs double.

Tip: Some of you lost the 2 in the original production function which is given as

𝑄(𝐾, 𝐿) = 2𝐾0.4𝐿0.6. Be careful in your calculations.

ii. What kind of return to scale does this production exhibit? Explain your answer

[5 marks]

We have already shown this in part (i); since output doubles when inputs double,

output is proportional to inputs, and thus the function exhibits constant return to

scale. We could also show this by adding the exponents: 0.4 + 0.6 = 1.

This indicates constant returns to scale.

Tip: Remember to explain your answer, as specified in the question.

General tips: While this assignment was on average answered well (with an

approximate average mark of 70%), many students lost marks for not labelling

graphs, for not showing workings and for not providing an explanation. In addition

to the actual answers, you also need to pay attention to how you answer the

questions; such as labelling graphs, showing workings and providing explanations,

otherwise you will lose marks. Note that this is true for exams as well; you will

lose marks for not labelling your graphs, showing workings or providing

explanations in the exam.

All the best for assignment 2. Remember to read the question carefully and be

sure to answer what the question asks. Always label graphs and show workings.

Don’t hesitate to contact your tutor if there is a question that requires clarity or

as explanation. Also, engage with your study guide and the textbook to obtain an

understanding. Good luck!

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