Core Consumer Theory (CCT) Flashcards
Explain the 5 axioms of consumer theory.
1) Completeness - A consumer can establish a preference order for all bundles.
2) Transitivity - Preferences are well-behaved, meaning if B1>B2 and B2>B3, then B1>B3.
3) Continuity - If B1>B3 and there lies a bundle sufficiently close to B3 (call it B2), then B1>B2.
4) Monotonicity - More is preferred to less.
5) Convexity - Averages are preferred to extremes. Also, all points in a straight line joining any 2 points must also be in that set.
Explain how monotonic transformations relate to Marshallian demand.
If we transform u(x) to v(u), then it is a positive transformation if v’(u)>0. Also, the 2 Marshallian demand curves will be the same, however, not all properties (e.g: diminishing marginal utility) will necessarily be the same.
When is a utility function said to be homothetic?
When the MRS and slope of the IC’s are the same, meaning that when income increases (whilst keeping the price ratio the same), goods are consumed in the same proportion.
Explain the 5 types of utility functions.
1) Cobb-Douglas - u(x,y) = (x^c)(y^d)
2) Perfect substitutes - u(x,y) - x+2y. It is a linear function with a constant MRS and no tangency solution.
3) Perfect complements - u(x,y) = min{x,2y}. It was a right-angled IC that is parallel to both axis’ and has no tangency solution.
4) Quasi-Linear - u(x,y) = x+ln(y). One of the goods does not have an income effect as Marshallian demand will not be a function of income (m).
5) Stone-Geary - u(x,y) = (x-z)^c (y-v)^d. Also does not have a tangency solution.
Explain how to recognise the difference between the Slutsky and Hicksian decomposition of the Slutsky equation.
-For the Hicksian decomposition, we only have 2 IC’s. We draw our compensated line (with point c) so that it is tangential to the original IC and parallel to the new budget line (the one with new prices), giving us our own and cross-income and substitution effects.
-For the Slutsky decomposition, there is 3 IC’s. We draw our compensated budget line so that it is parallel to the new budget curve and goes through our original point, a, giving us our own income and substitution effects.
What is a gross substitute/complement?
Good Y is a sub/complement of good X if an increase in the price of X means that MARSHALLIAN demand for good Y increases/decreases. We can recognise the Marshallian demand as this does not include the compensated IC/budget curve (point C).
What is a net substitute/complement?
Good Y is a sub/complement of good X if an increase in the price of X means that HICKSIAN/SLUTSKY demand for good Y increases/decreases. We can recognise the Hicksian/Slutsky demand as this is the point C on the new IC/budget line.
What is a net substitute/complement?
Good Y is a sub/complement of good X if an increase in the price of X means that HICKSIAN/SLUTSKY demand for good Y increases/decreases. We can recognise the Hicksian/Slutsky demand as this is point C on the new IC/budget line.
What is compensated variation?
CV is the income required to return the consumer to the original level of utility, following a price change, meaning it is the difference in new and original income required. To calculate this, keep px and py (do not sub in the prices) in order to form an equation for x and y in terms of m… then, we can sub in this to the utility function and set it equal to the original level of utility, rearranging to solve for x and y and then subbing this in to the income equation.
What is the equivalent variation?
EV is the income required to achieve the new utility but at the old prices.
What is the difference between Direct and Indirect Revealed Preference (DRP/IRP)?
DRP - if A is chosen when B is affordable then A is DRP to B.
IRP - if A is chosen when B is affordable and B is chosen over C then A is IRP to C.
