| Date | May 2018 | Marks available | 1 | Reference code | 18M.3.HL.TZ0.1 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Label and Draw | Question number | 1 | Adapted from | N/A |
Question
Note that widgets and pidgets are imaginary products.
In the country of Burbia, the demand and supply of widgets are given by the functions
Qd = 249 − 4P
Qs = 150 + 14P
where Qd is the quantity demanded per month, Qs is the quantity supplied per month and P is the price per widget in dollars ($).
The final of the 2018 Football World Cup is expected to be held in the Luzhniki stadium, Moscow.
The capacity of the stadium is 80 000. The expected cost of holding the final is US$12 million, which is not dependent on the number of people attending the match. All tickets will be sold for the same price.
Calculate the equilibrium price and quantity per month.
Calculate the excess demand/excess supply (state which of these) at a price of $8.50.
Calculate the price at which excess demand of 18 widgets would result.
A demand curve is drawn under the assumption of ceteris paribus.
Using an example, outline why the assumption of ceteris paribus is necessary when analysing the effect of a change in price on the quantity demanded of a product.
Widgets and Pidgets have negative cross price elasticity of demand (XED).
Explain how the demand function for Widgets, Qd = 249 − 4P, is likely to change as a result of an increase in the price of Pidgets.
The demand for widgets is considered to be unit elastic at the current price.
Outline the meaning of the term unit elastic demand.
Explain two determinants of the price elasticity of demand (PED).
Two products are in competitive supply. Using an example, outline how the supply for one of them is likely to be affected by an increase in the price of the other.
State the value of the price elasticity of supply (PES) for tickets to the 2018 Football World Cup final.
On the diagram draw and label the supply curve for tickets at the 2018 Football World Cup final.
Draw and label the marginal revenue (MR) curve for the 2018 Football World Cup final.
Using the diagram and your answers to parts (j) and (k), explain how the organizers could achieve their goal of profit maximisation.
Markscheme
249 − 4P = 150 + 14P
99 = 18P
Any valid working is sufficient for [1].
P = $5.50, Q = 227
An answer of 5.50, 227 (without working) is sufficient for [1].
Qd = 249 − 4 × 8.50 = 215
Qs = 150 + 14 × 8.50 = 269
Any valid working is sufficient for [1].
There will be excess supply or a surplus of 54.
An answer of 54 (without working) is sufficient for [1].
249 − 4P = 150 + 14P + 18
81 = 18P
Any valid working is sufficient for [1].
P = $4.50
An answer of 4.50 (without working) is sufficient for [1].
Price elasticity of supply = 0
For a vertical supply curve, labelled, at 80 000 tickets.
For an accurate, labelled MR curve.
Examiners report
Syllabus sections
- 17M.3.HL.TZ0.01c.ii: Determine: average revenue when output is equal to 6 units.
- 17M.3.HL.TZ0.01c.i: Determine: marginal revenue when output is equal to 4 units.
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18N.2.HL.TZ0.3a.ii:
Define the term total revenue indicated in bold in the text (paragraph [6]).
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19N.3.HL.TZ0.1d.ii:
Draw and label the marginal revenue (MR) curve for corn for an individual farmer in Nissos on the grid below.
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19M.3.HL.TZ0.2d:
Calculate the change in expenditure on imported oranges as a result of the increase in demand.
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21M.3.HL.TZ0.3f.ii:
Sketch the total revenue (TR) curve for firms in the widget industry.
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17M.3.HL.TZ0.01d:
Calculate the marginal revenue resulting from a fall in price from $8 to $6.
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19M.3.HL.TZ0.1i:
Draw and label the marginal revenue (MR) curve for the concert on Figure 3.
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19M.3.HL.TZ0.1j:
Calculate the maximum revenue that could be earned from selling tickets for the concert.
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21M.3.HL.TZ0.3f.i:
Sketch the marginal revenue (MR) curve for firms in the widget industry.
