ECO362H1 Study Guide - Final Guide: Competitive Equilibrium, Root Mean Square, Briey
NAME:
STUDENT NUMBER:
UNIVERSITY OF TORONTO
Faculty of Arts and Science
ECO362H1F – Economic Growth
Instructor: Stephen Ayerst
Duration: 120 Minutes
Instructions: This is a closed-book exam which is worth 120 points. There are 16 pages
in total. Non-programmable calculators are allowed. Read the entire question before
answering. Make all the extra assumptions you consider necessary, but make sure to state
them clearly. Be concise in your answers. Good luck!
Question 1 (40 Points)
Consider the following preferences:
u(ca, cn) = αln(ca−¯a) + (1 −α) ln(cn+ ¯n)
where ¯a≥0and ¯n≥0. Households supply labour inelastically and receive a wage was
their only source of income. The population is normalized to unity, N= 1.
Production is given by
Ya=AaNaYn=AnNn
(a) Define the household’s problem and take the first-order conditions. (6 points)
1
(b) Define the firms’ problems. (Hint: set pa=pand normalize pn= 1)(6 points)
(c) Define the competitive equilibrium. (6 points)
2
(d) Characterize the competitive equilibrium. In the expressions for c∗
aand c∗
nexplain the
role of ¯aand ¯n. Solve for the expenditure share of the agricultural sy
aand non-agricultural
sy
ngoods. (8 points)
3
Document Summary
Instructions: this is a closed-book exam which is worth 120 points. Make all the extra assumptions you consider necessary, but make sure to state them clearly. Consider the following preferences: u(ca, cn) = ln(ca a) + (1 ) ln(cn + n) where a 0 and n 0. Households supply labour inelastically and receive a wage w as their only source of income. The population is normalized to unity, n = 1. Yn = annn (a) de ne the household"s problem and take the rst-order conditions. (6 points) 1 (b) de ne the rms" problems. (hint: set pa = p and normalize pn = 1) (6 points) (c) de ne the competitive equilibrium. (6 points) In the expressions for c role of a and n. Solve for the expenditure share of the agricultural sy sy n goods. (8 points) a and c n explain the a and non-agricultural. Graph the allocation of labour over time across the two sectors.
