Short Answer Questions (50 points)
1. (25 points) Alfred Marshall spends H hours awake, which he can spend writing his book Principles of
Economics (labor) or solving economic problems (leisure). For each 10 written pages he gets paid a
wage of w and it takes him 2 hours to write 10 pages. He spends his income in a consumption good (C)
that has a price of PC. His utility is given by the following equation:
U(l,C)=a-l- 512+bc
where a, b > O are parameters.
(a) (1 point) Alfred wants to maximize his utility by choosing consumption (C), labor (L) and leisure
(1) subject to his time constraint and his budget constraint. 7Write down the problem that Alfred
solves.
(b) (2 points) Solve for Marshall’s Marshallian demands for leisure and consumption.
(c) (4 points) John Hicks, Alfred’s best friend, tells him that if he Lninimizes the nominal value of his
time awake (wH) subject to at least having a level of utility of U, and the labor market constraint
he would get exactly the same demand for leisure. Write down the problem that Hicks proposesl.
Write the Lagrangean associated with the problemz. Take first order conditions and verify that
Marshall’s Hicksian demand for leisure is the same as his Marshallian demand for leisure.
(d) (2 points) Give an economic interpretation of the Lagrange multiplier associated with Marshall’s
utility constraint.
(e) (3 points) If Marshall gets offered a higher wage, what would happen to the number of hours he
spends solving economic problems (leisure)? Draw a graph showing your results. Label the initial
point as (A), the point with the substitution effect as (B) and the final point as (C).
(f) (2 points) Derive Alfred’s labor supply, draw its graph and give an interpretation of its shape using
the income and substitution effect.
(g) (5 points) Marshall desires to improve the mathematical rigour of economics and transform it into
a more scientific profession. He decides to sleep one hour less than he used to before. Explain how
his Optimal leisure, labor and consumption change, and give an interpretation using the income and
substitution effect. Draw a graph showing your results. Label the initial point as (A), the point
with the substitution effect as (B) and the final point as (C).
(h) (5 points) Analyze the cross-price effect of an increase in the price of the consumption good on
Marshall’s optimal leisure choice. Then, analyze the own-price effect of an increase in the price
of the consumption good on Marshall’s optimal consumption. In both cases use the income and
substitution effect to justify your results3. Draw a graph showing your results. Label the initial
point as (A), the point with the substitution effect as (B).and the final point as (C).
(i) (1 point) How does Marshall’s maximal utility (indirect utility) changes with respect to the param-
eter b? Give an economic interpretation to your result.