Exam graphs · Lectures 2–5 · every graph they can ask you to draw
Exam Graph Drill
Each graph the exam can ask for, with a numbered drawing recipe, the mistakes that lose marks, and the live diagram to check your drawing against. Draw each one on paper first, then compare.
By the end you can
Draw every Lecture 2–5 graph from memory with full labels
Know which curve moves, which point stays fixed and which way the arrow points
Write the one-sentence conclusion that goes under each graph
Rules for every graph
Practise like this: read the recipe, draw on paper, then open the diagram and compare.
1 · Market equilibrium and one shift
Asked as: “Show the effect of a rise in income / input price / tastes on the market for X.”
Diagram · Income rises (normal good)
demand dsupply sbefore the shift
Buyers have more money, so they want more at every price. Income is a barred determinant of demand, so demand shifts right.
Price
–
Quantity
–
Press “Show shift” to move the curve.
2 · Both curves shift
Asked as: “Demand rises and supply falls at the same time. What happens?”
Diagram · Hibiscus: tax up (t ↑) and tastes up (T ↑)
demand dsupply sbefore the shift
The tax shifts supply left. Hibiscus becoming fashionable shifts demand right. Switch which shift is bigger and watch what changes.
Price
–
Quantity
–
Press “Show shift” to move the curve.
3 · Price above or below equilibrium
Asked as: “At price P1, show the excess supply (or shortage).”
Diagram · Out of equilibrium
Quantity demanded
q₁ = 50
Quantity supplied
q₂ = 100
Gap
50 unsold
At P₁ buyers take only q₁ (point A) but sellers bring q₂ (point B). Unsold stock piles up, sellers cut prices, and P falls back to pᵉ.
4 · Elasticity on a straight demand line
Asked as: “Show where demand is elastic, unit elastic and inelastic.”
Diagram · Elasticity along a straight demand lineq = 35 − 0.008P
Quantity demanded q
11.00
E = −0.008 · P / q
-2.18
Classification
elastic
Elastic: a 1% price rise cuts quantity by 2.18%. The slope is the same everywhere on the line, but P/q is not, so elasticity changes as you slide.
Diagram · Demand shapes and elasticity|E| = 0 everywhere
A vertical demand curve: buyers take the same quantity whatever the price (insulin for a diabetic is the usual example). A price change moves along the line but quantity does not change at all, so the percentage change in Q is 0 and E = 0. A price rise always raises total revenue.
5 · Indifference curves
Asked as: “Draw indifference curves for (a) Cobb-Douglas, (b) perfect substitutes, (c) perfect complements” or “Show that two indifference curves cannot cross.”
Diagram · Indifference mapU = √(XY)
Bundle (X, Y)
(30, 43)
MRS of X for Y
1.44
MRS = Y/X = 43.2/30.0 = 1.44. Bowed in toward the origin: the more X you already have, the less Y you will give up for one more unit of X. That is a diminishing MRS.
6 · Total and marginal utility
Asked as: “Draw TU and MU for a good with diminishing marginal utility.”
Diagram · Total and marginal utilityU = 10√x, MU = 5/√x
Total utility U(x)
50.0
Marginal utility MU(x)
1.00
Marginal utility is the slope of the total utility curve. As x grows, total utility keeps rising (MU stays positive, so more is better) but more and more slowly: this is diminishing marginal utility. Total utility would only fall if MU turned negative.
7 · Budget line shifts
Asked as: “Show the effect of a rise in income / in Px / in Py on the budget line.” The lecturer’s favourite.
Interactive · Budget linePx·x + Py·y = I
budget linestarting line (I = 800, Px = 20, Py = 40)budget set
Food intercept I/Px
40
Clothing intercept I/Py
20
Slope −Px/Py
-0.5
1 food costs (clothing)
0.5
This is the starting line: I = 800, Px = 20, Py = 40. Move a slider and the dashed copy stays behind for comparison.
Cost of (15, 10) = 20·15 + 40·10 = 700. Affordable, with 100 left over: inside the budget set.
Check your understanding
I=800, Px=20, Py=40. Px rises to 40. How do you draw the new line?
8 · Kinked budget lines
Asked as: “Draw the budget set with a quantity discount / rationing / food stamps.”
Diagram · Kinked and special budget setsPx = 20 up to 20 units, 10 after
original line: 20x + 40y = 800new budget line
The first 20 units of food cost 20 each, every unit after that costs 10. Up to x = 20 the line has the normal slope −20/40 = −0.5. At the kink (20, 10) the consumer has spent 400 on food. After it the slope is −10/40 = −0.25, so the line gets flatter and reaches the food axis at 20 + 400/10 = 60 instead of 40. The kink points outward, so this budget set is not convex.
9 · The optimal choice (tangency)
Asked as: “Show the consumer’s optimal basket and explain why other baskets on the budget line are not optimal.” Use the lecturer’s letters.
budget lineindifference curvesslope of the curve (MRS)
Moving in from B and from C ends at basket A = (20, 10), where U₂ = 200 just touches the budget line. At point A the slope of the budget line equals the slope of the indifference curve: MRS = y/x = 10/20 = 0.5 = Px/Py. D on U₃ = 300 would be better, but it lies outside the budget line: unaffordable.
10 · Corner and kink solutions
Asked as: “Show the optimum for perfect substitutes / perfect complements.”
Diagram · Corner and kink solutionsU = x + y, 20x + 40y = 800
budget lineindifference curves
Indifference curves are straight lines with slope −1, steeper than the budget line (−0.5) everywhere. Utility per lira: 1/20 on food beats 1/40 on clothing, so the consumer slides all the way to the food intercept: A = (40, 0), U = 40. Draw A on the x-axis; the curve through A touches the line only at its end.
Final self-test
Check your understanding
In a budget line question, which intercept stays fixed when the price of clothing (y) falls?
Check your understanding
On the optimal-choice graph, the consumer is at C, below and to the right of A, on the budget line. What is true at C?