Date | May 2019 | Marks available | 1 | Reference code | 19M.3.HL.TZ0.1 |
Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
Command term | Identify | Question number | 1 | Adapted from | N/A |
Question
Note that widgets are an imaginary product.
In Country X, the supply and demand for widgets are given by the functions
Qs = − 45 + 4.5P
Qd = 180 − 3P
where P is the price per widget in dollars ($), Qs is the quantity of widgets supplied (thousands per year) and Qd is the quantity of widgets demanded (thousands per year).
The supply (S) and demand (D) functions are represented in Figure 1.
An increase in costs of production has resulted in a new supply function:
Qs1 = − 60 + 3P
Figure 2 shows the demand for and supply of widgets in Country Y.
Figure 2
The government of Country Y decides to impose an indirect tax of $10 per widget.
A music concert is to take place in Country Z. 40 000 tickets are available for the concert. Figure 3 shows the demand (D) for tickets at this concert.
Figure 3
The fixed costs for the concert have been calculated as $3 million, while it is expected that there will be no variable costs.
Identify the slope of the supply curve.
Outline the reason why the quantity supplied increases as the price rises.
Draw and label the new supply curve on Figure 1.
Using your answer to part (c), outline the reason why an increase in costs of production has resulted in a new supply function.
Calculate the change in producer surplus resulting from the increase in costs of production.
Define the term price elasticity of supply.
The time taken to produce goods is an important determinant of the price elasticity of supply.
Apart from time, explain two factors which influence the price elasticity of supply.
With reference to Figure 2, explain how the incidence of taxation on consumers and/or producers will be influenced by the price elasticity of supply.
Draw and label the marginal revenue (MR) curve for the concert on Figure 3.
Calculate the maximum revenue that could be earned from selling tickets for the concert.
Calculate the average fixed cost per ticket if all tickets are sold.
Assuming the event organizers aim to maximize profit, calculate the profit that will be made from the concert.
Markscheme
Slope = 4.5 OR + 4.5 (or 1/4.5 or 2/9)
An answer of 4.5 or + 4.5 (or 1/4.5 or 2/9) without any working is sufficient for [1].
NB Responses which outline only that producers are “more able to afford” to produce more should not be rewarded.
Award [1] for an accurate, labelled supply curve.
NB Responses which make reference to producers being “less able to afford” resources should not be rewarded.
Reference to the need to cut costs may be rewarded at level 1, but if the candidate refers to producers being unable to afford to supply, this should not be rewarded.
An accurate numerical example, referring explicitly to data in the graph, should be rewarded.
(0.5 × 20 × 60 000) − (0.5 × 20 × 90 000)
Any valid working is sufficient for [1].
= −$300 000 (or a decrease of $300 000)
An answer of −$300 000 or −300 000 without any working is sufficient for [1].
The time taken to produce goods is an important determinant of the price elasticity of supply.
Factors may include:
- whether the firm has excess (or unused, or spare) capacity available: if it does, then increasing output will be easier so supply will be more price elastic
- possibility of storage: the greater the ability to store stocks, the more price elastic supply will be as firms can draw from stocks to increase the quantity supplied
- mobility of factors of production: the easier it is for a producer to switch resources from one use to another, the easier it will be to increase the quantity supplied in response to an increase in the price of the product, so supply will be more elastic (the ease with which technology can be implemented/applied could be an example
of this) - the rate at which costs rise as output increases – the faster/higher the rate, the lower the PES (NB “costs of production” should not be rewarded)
- the nature of the product eg for agricultural products, the time lag between planting and harvest is relatively long, so supply would be relatively price inelastic in the short term.
Any other reasonable response should be rewarded.
Award [1] for an accurate, labelled marginal revenue (MR) curve.
150 × 30 000
Any valid working is sufficient for [1].
= $4 500 000
An answer of $4 500 000, 4 500 000, $4.5 million or 4.5 million without any working is sufficient for [1].
OFR applies from part (i), depending on where the MR curve cuts the x axis.
$3 million / 40 000 = $75
An answer of $75 or 75 is sufficient for [1].
Award [1] if the candidate identifies that profit will be maximized where:
MC = MR
OR
MC = 0
OR
TR − TC is maximized
ie at 30 000 tickets and a price of $150.
TR = 30 000 × $150 = $4.5 million
TC = $3 million
Profit = 4.5 million − 3 million
Any valid working is sufficient for [1].
= $1.5 million
An answer of $1.5 million or 1.5 million or 1 500 000 without any working is sufficient for [1].
OFR applies, provided either TR or TC is calculated correctly.
Examiners report
Most candidates were able to identify the slope. A significant minority identified as 2/9 or 0.22, which was rewarded given the generally accepted convention.
Many students simply stated the Law of Supply, or justified with reference to revenue rather than profit. In perfect competition revenue would increase with an increase in output whether price increased or not, so reference to revenue only was deemed a Level 1 response.
Generally well-answered, with few errors.
Few candidates demonstrated an understanding of the underlying concepts relating to supply theory. Although the vast majority stated that “the costs of production” is a determinant of supply, few were able to explain why a new supply function arises with reference to incentives or profitability.
Although calculation of “300” was performed successfully by many, omission of “000”, “$” or reference to “a decrease” was extremely common. Several responses calculated the initial PS as 800 or 1350.
Generally well-answered, although lower achieving responses merely stated or described the formula, while some referred to the responsiveness of producers, without referring to supply or quantity supplied.
The majority of candidates were able to refer to “ability to store”, “mobility of factors of production” or “the rate at which costs of production increase” as factors other than time which influence PES. Lower achieving responses stated rather than explained, while some made basic errors such as explaining that factor mobility is the ability to physically move machinery. Others confused PES with PED and referred to factors such as the degree of necessity.
The majority of candidates encountered difficulty with this question. Most stated that supply was perfectly inelastic, while a significant number identified the relevant learning outcome, “Explain, using diagrams, how the incidence of indirect taxes on consumers and firms differs, depending on the price elasticity of demand and on the price elasticity of supply” – but could not apply the theory to the context provided. As PES = 0, the producers would bear the whole incidence. Many candidates erroneously referred to a decrease on demand resulting from a higher price.
The majority of candidates were able to draw a downward-sloping MR curve with double the slope of the demand curve, intersecting the vertical axis at $300, but a common error was for the curve to intersect the horizontal axis at 40 000 (the number of tickets available) rather than 30 000.
The majority of candidates recognized that revenue is maximized where MR = 0 and therefore earned full marks here, either correctly or with application of the Own Figure Rule (OFR). A significant number, however, provided an answer of $4 million without any justification.
Generally well-answered, with a small number of basic errors.
Higher achieving responses recognised that MC = 0, and so to meet the profit-maximizing condition MR must also be zero (i.e. at the revenue-maximizing level of output). Lower achieving responses appeared to assume that revenue maximization is equivalent to profit maximization and calculated accordingly.