ECS2601
EXAM PACK
,ECS2601 ASSIGNMENT 2 SEMESTER 2 2025
Question 1 (10 marks)
1.1 Why MRS = price ratio at utility maximum (2 marks)
At the consumer’s optimum (given a budget constraint), the highest attainable
indifference curve is tangent to the budget line. Tangency means the slopes are
equal: [ \text{MRS}_{X,Y} = \frac{MU_X}{MU_Y} = \frac{P_X}{P_Y}. ] Interpretation: if
MRS differed from the price ratio the consumer could reallocate spending to
increase utility — equality means no marginal trade (between X and Y) can raise
utility without violating the budget.
1.2 Differentiate between any two (4 marks)
I’ll do (a) Positive vs Normative and (d) Ordinal vs Cardinal rankings.
Positive vs Normative
Positive analysis describes “what is” — objective statements that can be
tested (e.g., “a tax increase will reduce consumption of X”).
Normative analysis prescribes “what ought to be” — value judgments that
cannot be proven true or false without a value stance (e.g., “the government
should tax X to reduce inequality”).
Ordinal vs Cardinal rankings
Ordinal ranking gives order of preferences (A preferred to B preferred to C)
but not the magnitude of differences. Indifference curves use ordinal utility.
Cardinal ranking assigns numerical utility measures that are meaningfully
comparable in magnitude (e.g., utility of 100 vs 50 means twice as much).
Modern consumer theory typically uses ordinal utility.
1.3 Shape of indifference curves & graph (4 marks)
(a) Household’s choice of two consumables per week
Reasoning: two distinct consumables (e.g., bread and milk) are typically
imperfect substitutes with diminishing marginal rate of substitution.
Indifference curves are convex to the origin (bowed in) — reflecting
, diminishing MRS: as you give up more of X for Y, you require progressively
more Y to compensate.
Graph: see the Convex IC curve in the first plot (labelled “Convex IC
(consumables)”).
(b) Two similar pizzas bought at different takeaway stores (same # of slices)
If pizzas from Store A and Store B are very similar and consumers are willing
to substitute one-for-one, they behave like perfect substitutes → indifference
curves are straight lines (linear), slope constant. If they are identical,
consumer indifferent to mix, so linear ICs with constant slope.
Graph: see the Linear IC lines in the first plot (labelled “Linear IC (pizza;
perfect substitutes)” and a higher linear IC).
Question 2 (15 marks)
2.1 Income and substitution effects when price rises (qualitative — 4
marks)
For each good describe expected size of substitution and income effects:
(a) Salt
Salt is a very small share of spending and a necessity with few close
substitutes (for salt there are not true substitutes for seasoning). Demand is
highly inelastic.
Substitution effect: small (there aren’t many close substitutes in practice).
Income effect: very small (price change uses tiny share of budget). → Overall
small change in quantity demanded.
(b) Housing (rent / shelter)
Large share of budget and often few short-run substitutes (moving is costly).
Substitution effect: can be moderate (over time you can substitute
smaller/cheaper housing), but short-run substitution small.
Income effect: large — price change on a big share of budget changes real
purchasing power significantly. → Large income effect; substitution effect
smaller short-run but may grow long-run.
(c) Theatre tickets
, Discretionary good with close substitutes (movies, streaming, other leisure).
Substitution effect: can be large (if price rises, consumers substitute to other
entertainment).
Income effect: moderate to small (tickets are usually a modest share, but for
some consumers could be significant). → Expect a relatively large
substitution effect and moderate income effect; demand relatively elastic
(for non-fans).
(d) Food (broadly)
Necessity with many varieties; overall staple: inelastic overall but some items
within food are elastic.
Substitution effect: moderate — consumers substitute within food categories
(switch brands), but not away from calories entirely.
Income effect: moderate (food is a significant budget share especially for
lower-income households). → Total change moderate; staples less
responsive, luxury food items more responsive.
2.2 Connie’s budget line (11 marks total: 7 graph + 4 slope)
Given:
Income (M=R10,000)
Price shelter (P_s = R50) per m²
Price food (P_f = R100) per kg
Food on vertical axis, Shelter on horizontal.
Compute intercepts (B1 base):
Shelter intercept (horizontal) = (M/P_s = 10, = 200) m².
Food intercept (vertical) = (M/P_f = 10, = 100) kg.
Slope of budget line = (-P_f / P_s = -100/50 = -2.)
Scenarios & intercepts (these are plotted together in the budget-lines plot):
B1 (Base): Shelter intercept = 200 m², Food intercept = 100 kg, slope = −2.
B2 (Ps falls to 40): Shelter intercept = (10,000/40 = 250) m²; Food intercept
unchanged = 100 kg; slope = −100/40 = −2.5. (Budget line rotates outward
around vertical intercept — more shelter affordable.)
EXAM PACK
,ECS2601 ASSIGNMENT 2 SEMESTER 2 2025
Question 1 (10 marks)
1.1 Why MRS = price ratio at utility maximum (2 marks)
At the consumer’s optimum (given a budget constraint), the highest attainable
indifference curve is tangent to the budget line. Tangency means the slopes are
equal: [ \text{MRS}_{X,Y} = \frac{MU_X}{MU_Y} = \frac{P_X}{P_Y}. ] Interpretation: if
MRS differed from the price ratio the consumer could reallocate spending to
increase utility — equality means no marginal trade (between X and Y) can raise
utility without violating the budget.
1.2 Differentiate between any two (4 marks)
I’ll do (a) Positive vs Normative and (d) Ordinal vs Cardinal rankings.
Positive vs Normative
Positive analysis describes “what is” — objective statements that can be
tested (e.g., “a tax increase will reduce consumption of X”).
Normative analysis prescribes “what ought to be” — value judgments that
cannot be proven true or false without a value stance (e.g., “the government
should tax X to reduce inequality”).
Ordinal vs Cardinal rankings
Ordinal ranking gives order of preferences (A preferred to B preferred to C)
but not the magnitude of differences. Indifference curves use ordinal utility.
Cardinal ranking assigns numerical utility measures that are meaningfully
comparable in magnitude (e.g., utility of 100 vs 50 means twice as much).
Modern consumer theory typically uses ordinal utility.
1.3 Shape of indifference curves & graph (4 marks)
(a) Household’s choice of two consumables per week
Reasoning: two distinct consumables (e.g., bread and milk) are typically
imperfect substitutes with diminishing marginal rate of substitution.
Indifference curves are convex to the origin (bowed in) — reflecting
, diminishing MRS: as you give up more of X for Y, you require progressively
more Y to compensate.
Graph: see the Convex IC curve in the first plot (labelled “Convex IC
(consumables)”).
(b) Two similar pizzas bought at different takeaway stores (same # of slices)
If pizzas from Store A and Store B are very similar and consumers are willing
to substitute one-for-one, they behave like perfect substitutes → indifference
curves are straight lines (linear), slope constant. If they are identical,
consumer indifferent to mix, so linear ICs with constant slope.
Graph: see the Linear IC lines in the first plot (labelled “Linear IC (pizza;
perfect substitutes)” and a higher linear IC).
Question 2 (15 marks)
2.1 Income and substitution effects when price rises (qualitative — 4
marks)
For each good describe expected size of substitution and income effects:
(a) Salt
Salt is a very small share of spending and a necessity with few close
substitutes (for salt there are not true substitutes for seasoning). Demand is
highly inelastic.
Substitution effect: small (there aren’t many close substitutes in practice).
Income effect: very small (price change uses tiny share of budget). → Overall
small change in quantity demanded.
(b) Housing (rent / shelter)
Large share of budget and often few short-run substitutes (moving is costly).
Substitution effect: can be moderate (over time you can substitute
smaller/cheaper housing), but short-run substitution small.
Income effect: large — price change on a big share of budget changes real
purchasing power significantly. → Large income effect; substitution effect
smaller short-run but may grow long-run.
(c) Theatre tickets
, Discretionary good with close substitutes (movies, streaming, other leisure).
Substitution effect: can be large (if price rises, consumers substitute to other
entertainment).
Income effect: moderate to small (tickets are usually a modest share, but for
some consumers could be significant). → Expect a relatively large
substitution effect and moderate income effect; demand relatively elastic
(for non-fans).
(d) Food (broadly)
Necessity with many varieties; overall staple: inelastic overall but some items
within food are elastic.
Substitution effect: moderate — consumers substitute within food categories
(switch brands), but not away from calories entirely.
Income effect: moderate (food is a significant budget share especially for
lower-income households). → Total change moderate; staples less
responsive, luxury food items more responsive.
2.2 Connie’s budget line (11 marks total: 7 graph + 4 slope)
Given:
Income (M=R10,000)
Price shelter (P_s = R50) per m²
Price food (P_f = R100) per kg
Food on vertical axis, Shelter on horizontal.
Compute intercepts (B1 base):
Shelter intercept (horizontal) = (M/P_s = 10, = 200) m².
Food intercept (vertical) = (M/P_f = 10, = 100) kg.
Slope of budget line = (-P_f / P_s = -100/50 = -2.)
Scenarios & intercepts (these are plotted together in the budget-lines plot):
B1 (Base): Shelter intercept = 200 m², Food intercept = 100 kg, slope = −2.
B2 (Ps falls to 40): Shelter intercept = (10,000/40 = 250) m²; Food intercept
unchanged = 100 kg; slope = −100/40 = −2.5. (Budget line rotates outward
around vertical intercept — more shelter affordable.)
