lecture_5_for_students_

# lecture_5_for_students_ - Lecture 5 Demand Click to edit...

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Click to edit Master subtitle style 1/1/11 Demand Lecture 5

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1/1/11 We learned how to maximize the utility of a consumer considering the budget constraint. Assuming the strictly convex indifference curves, the optimal point is at the tangency point of the budget and indifference curves, and the consumer uses the positive amounts of both goods (MRS=MRT). Now the question is finding out how the consumer’s consumption changes when the price of for example one of the goods changes
1/1/11 Assume a consumer is consuming q1 and q2. Her utility function is U=U(q1, q2)= and her budget constraint is 12q1+35q2=419. Find the optimal point or where utility is maximized. 24 . 0 2 76 . 0 1 q q Deriving Demand Curve for q1 ) 24 . 0 and 76 . 0 ( 76 . 0 2 76 . 0 1 2 24 . 0 2 24 . 0 1 1 - - = = q q MU q q MU q q 12) (P 7 . 26 1 8 . 2 2 : e Point 2 35 2 ) 11 . 9 ( 12 2 35 1 12 419 11 . 9 35 12 24 . 0 76 . 0 : 1 1 2 1 1 2 2 1 = = + = + = = = - = = - = - = q and q q q q q q q MRT q q MU MU MRS Answer q q

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1/1/11 Assume P1↓ (from 12 to 6) => budget rotates (L1 to L2) =>find the new equilibrium from MRS=MRTnew => e2: q1*=44.5, q2*=4.3 (p1=6) Assume P1↓ further (from 6 to 4) => budget rotates => L2 to L3 =>e3: q1*=58.9 , q2*=5.2 (p1=4) Using the amount of q1 and P1 in equilibrium points Deriving Demand Curve for q1
1/1/11 Deriving Demand Curve 2) P1↓ (\$6) => e2 ( p1=6 , q1=44.5 ) 3) P1↓ (\$4) => e3 ( p1=4 , q1=58.9 ) 4) Price consumption curve and total effect 1) At original equi or e1 ( p1=12 , q1=26.7 ) q 1 q 2 q1 P 1 Demand For q1

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1/1/11 Assume a consumer is consuming q1 and q2. Her utility function is U=U(q1, q2)= and her budget constraint is 12q1+35q2=419. Find the optimal point or where utility is maximized. 24 . 0 2 76 . 0 1 q q ) 24 . 0 and 76 . 0 ( 76 . 0 2 76 . 0 1 2 24 . 0 2 24 . 0 1 1 - - = = q q MU q q MU q q 419) ( 7 . 26 1 8 . 2 2 : e Point 2 35 2 ) 11 . 9 ( 12 2 35 1 12 419 11 . 9 35 12 24 . 0 76 . 0 : 1 2 1 1 2 2 1 = = + = + = = = - = = - = - = I q and q q q q q q q MRT q q MU MU MRS Answer q q Income Increase and Engle Curve
1/1/11 Income Increase and Engle Curve L1 :12q1+35q2= 419 => e1 is the optimal point (q1=26.7 and I=419) Income ↑ to 628\$ ( e2 and L2) => (q1=38.2 and I=628) Income ↑ to 837\$ ( e3 and L3)=> (q1=49.1 and I=837) q 1 q 2 q1 I q 1 p 1 Change of income is IC C

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1/1/11 Example L 1 I 1 L 2 I 2 e1 e2 Pepsi Canada Dry q1 q2 Peps i Income Engle Curve for Pepsi I 1 I 2 q1 q2 Canada Dry (q2) and Pepsi (q1) are perfect substitutes for Mimi. Her utility function is U(q1,q2)=q1+q2. If P of Pepsi is less than Canada Dry, plot Mimi’s Engle curve for Pepsi.
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