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Microeconomia Corso E

Microeconomia Corso E. John Hey. Chapter 7 – what do we know?. Individual with given preferences and income m faces prices p 1 and p 2 for two goods:1 and 2. He or she is going to allocate his or her income buying quantities q 1 and q 2 of the two goods.

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Microeconomia Corso E

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  1. MicroeconomiaCorso E John Hey

  2. Chapter 7 – what do we know? • Individual with given preferences and income m faces prices p1 andp2 for two goods:1 and 2. • He or she is going to allocate his or her income buying quantities q1andq2 of the two goods. • What he or she buys/demands depends on her preferences. • The relationship between q1andq2 (the endogenous variables) and m, p1andp2 (the exogenous variables) is called the demand function.

  3. Chapter 7 – what do we know? • Cobb-Douglas with parameter a q1 = am/p1 and q2 = (1-a)m/p2 • Perfect Substitutes 1:a if p1/p2 < a thenq1 = m/p1 q2 = 0 if p1/p2 = a then.... ifp1/p2 >a thenq1 = 0q2 = m/p2 • Perfect Complements 1 with a q1=m/(p1 + ap2) and q2 =am/(p1 + ap2) • These formulas are in the promemoria.

  4. The optimal point • With indifference curves that are smoothly convex... • ... the optimal point is the point of tangency between the budget line and the highest possible indifference curve... • ...at which the relative price (the slope of the budget line) is equal to the marginal rate of substitution (the slope of the indifference curve).

  5. Are we economists or not? • Economists are ... • ... lazy ... • ... efficient. • In Chapter 7 income is in the form of money m. In Chapter 6, income is in the form of endowments of the two goods: e1and e2. • What is the money value of this endowment? Call it m. • We have m = p1e1+ p2e2. • Let us just replace m with p1e1+ p2e2 everywhere!

  6. From Chapter 7 we have • Cobb-Douglas with parameter a q1 = a( m )/p1 and q2 = (1-a)( m )/p2 • Perfect Substitutes 1:a if p1/p2 < a thenq1 = ( m )/p1 andq2 = 0 if p1/p2 = a then.... ifp1/p2 >a thenq1 = 0 andq2 = ( m )/p2 • Perfect Complements 1 with a q1= ( m )/(p1 + ap2) and q2 =a( m )/(p1 + ap2)

  7. Hence for Chapter 6 • Cobb-Douglas with parameter a q1 = a(p1e1+ p2e2)/p1 and q2 = (1-a)(p1e1+ p2e2)/p2 • Perfect Substitutes 1:a if p1/p2 < a thenq1 = (p1e1+ p2e2)/p1 andq2 = 0 if p1/p2 = a then.... ifp1/p2 >a thenq1 = 0 andq2 = (p1e1+ p2e2)/p2 • Perfect Complements 1 with a q1= (p1e1+ p2e2)/(p1 + ap2) and q2 =a(p1e1+ p2e2)/(p1 + ap2)

  8. Chapter 6 • Finished!

  9. Chapter 6 • We consider an individual who starts with an endowment of the two goods. • We find his gross demands for the two goods. • We analyse how these demands change when the prices and his income change. (These variables are exogenous for the individual). • These are called comparative static exercises.

  10. Chapter 6 • We start with an individual with Cobb-Douglas preferences with parameter a = 0.5. • The Maple/html file contains other examples: • Cobb-Douglas with parameter a = 0.3; • Stone-Geary; • Perfect Substitutes; • Perfect Complements. • The shape of the demand curve depends upon the preferences.

  11. Chapters 6 and 7 • We use two spaces: • The first: to show the preferences of the individual and the budget line: • q1on the horizontal axis and q2on the vertical axis. • The second: to show the effect of changes in an exogenous variable on the demand: • q1 (andq2 ) on the horizontal axis and the exogenous variable on the vertical axis.

  12. Chapter 6 • The indifference curves are given by the preferences. • The budget constraint is given by the individual’s income and the prices of the two goods. • We denote by (e1, e2) the endowment and by (q1, q2) the quantities chosen to consume. The budget line is given by the equation: • p1q1 + p2 q2 = p1e1 + p2e2 • This is a line with slope • - p1/ p2 • which passes through the endowment point.

  13. q2 the budget line: p1 q1 +p2 q2 = p1 e1 +p2 e2 (p1 e1 +p2 e2)/p2 has slope = -p1/p2 and passes through (e1,e2) e2 X (p1 e1 +p2 e2 )/p1 q1 e1

  14. Cobb-Douglas with parameter a = 0.5 U(q1, q2) = q10.5q20.5

  15. Chapter 6 – results • Cobb-Douglas with parameter a q1 = a(p1e1+p2e2)/p1 e q2 = (1-a)(p1e1+p2e2)/ /p2 • Perfect substitutes 1:a if p1/p2 < a then q1 = (p1e1+p2e2)/p1 q2 = 0 if p1/p2 = a then.... ifp1/p2 >a thenq1 = 0q2 = (p1e1+p2e2)/p2 • Perfetti complements 1 with a q1= (p1e1+p2e2)/(p1 + ap2) e q2 =a(p1e1+p2e2)/(p1 + ap2)

  16. Chapter 6 • Goodbye!

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