• Marshall’s colleague at Cambridge, John Neville Keynes (father of John Maynard Keynes) in The Scope and Method of Political Economy (1891):
  1. “Positive economics”: study of what is, and how the economy works (scientific)
  2. “Normative economics”: study of what should be
  3. “Art of economics”: related lessons learned from positive economics to normative goals determined in the normative branch

• Marshall famously kept mathematics to a minimum (in the appendices), focused on teachable graphs

• His definitions & concepts are not very precise or tidy, but practical

• Again, goal of appealing to businesspeople and the educated public, not technical specialists

• Instead of the sharp Classical division of land vs. labor vs. capital, Marshall: “the factors of production”

• For theory of the firm, “we shall have to study the expenses of a representative producer”

  • not a statistical average, but a realistically-surveyed firm of normal ability and access to technology

• Because economics can run no experiments like physics, must do so with theoretical constructs by assumption to approximate causal relationships in the complex economy

• Ceterus paribus, hold all else equal to investigate the likely consequences of a single change

• Isolate a single market and ignore (but don’t deny) interdependencies with other markets (substitutes, complements, inputs, outputs, etc.)

  • Yields a first approximation of the consequence of a single change

“Time is a chief cause of those difficulties in economic investigations which make it necessary for man with his limited powers to go step by step”

• It’s futile to argue whether demand or supply determines the price:

“We might as reasonably dispute whether it is the upper or under blade of a pair of scissors that cuts a piece of paper, as whether value is governed by utility or costs of production. It is true that when one blade is held still, and the cutting is effected by moving the other, we may say with careless brevity that the cutting is done by the second; but the statement is not strictly accurate, and is to be excused only so long as it claims to be merely a popular and not a strictly scientific account of what happens.”

• Demand, supply, and price are all interrelated and simultaneously determined

• Marshall: individuals desire goods because of the utility they provide
  • used additive utility functions: total utility simply is the sum of the quantity of each good consumed

$$U(x,y,z)=ax+by+cz$$

• This does not allow for complementarity and substitutability of goods in consumption
  • Modern utility functions, following Edgeworth and Fisher, are non-linear, e.g.
  • Allows for complementarity and substitutability

$$U(x,y,z)=x^a{y}^b{z}^c$$

• Marshall: assumed utility was measurable via prices

  • Didn't really like the way others used utility functions (not practical)
  • Example: if person pays $2 for A and $1 for B, A must yield twice the utility of B

• The marginal utility of a good is equal to its price times the “marginal utility of money”:

$$M{U}_a=p_a\ast M{U}_m$$

• Marginal utility of money $\left(M{U}_m\right)$: marginal utility received from last dollar spent (or earned, if we consider “savings” a good)

• Most important task: explain shape of demand curves: law of demand

“The amount demanded increases with a fall in price, and dminishes with a rise in price.”

• Diminishing marginal utility (Gossen’s first law) $⟹$ downward sloping demand

• Optimum condition for maximizing utility: equalize marginal utility of the last dollar spent on each good

  • Gossen’s second law/equimarginal principle:
  • Marshall: equates to the marginal utility of money, $M{U}_m$

$$\frac{M{U}_a}{p_a}=\frac{M{U}_b}{p_b}=\frac{M{U}_c}{p_c}=M{U}_m$$

• The “Cambridge cash-balance” approach to quantity theory of money, vs. Fisherian approach:

  • nominal money supply meets real money demand to determine price level

• Nominal demand for money balances: $M^D=kPy$

  • Real demand for money balances: $\frac{M^D}{P}=m^D=ky$

• Nominal supply of money: $M^S=M$

• Equilibrium: $M^D=M$, so $P=\frac{M}{ky}$

• $k$ is “desired” average level of nominal money balances $\frac{M}{Py}$ in long run

  • i.e. I hold “k%” of my (nominal) income as cash each period

• Depends on:

  • convenience of holding money
  • opportunity cost (other interest-earning investments)
  • money substitutes (checks, credit, etc)
  • inflation expectations
  • degree of business confidence

• This is what Marshall really meant by his “marginal utility of money” $M{U}_m$

• Recall Fisher’s equation of exchange: $MV=Py$^†

  • $V$ defined tautologically as $V=\frac{Py}{M}$
  • Velocity, “number of times a dollar changes hands”
  • $V=$ actual $\frac{Py}{M}$

• Marshall (and Cambridge approach) alternatively uses $k$

  • “Desired ratio of money balances to income”determined by real factors
  • Determined by real factors (independent of $M)$
  • $k=$ desired $\frac{Py}{M}$
  • $V$ adjusts to “desired $V$” implied by desired $k$