1. Alex spends his money on food, a normal good, and all other goods (also normal). Decompose the...

Question

1.
Alex spends his money on food, a normal good, and all other goods (also normal). Decompose the total effect of a decrease in food prices into substitution effects and income effects. (i.e. draw the graph)

2.If Maria’s utility function is U = 2q₁
^0.5+ q₂:

a.What are her demand functions for the two goods?

b.What are her income elasticity for the two goods?

c.What are her Engel Curve for the two goods?

3.Bill’s utility function is U = 2ln(q₁) + 2ln(q₂). What is his compensated demand function for q₁?

4.Siggi’s quasilinear utility function isU = 4ln(q₁₎
^{+ q₂. His budget for these goods is Y = 10. Originally, the prices are p₁= p₂= 1. However, the price of the first good rises to p₁= 2. Discuss the substitution, income, and total effect on the demand for q₁.}

5.If the inverse demand function for radios is p = a – bq, what is the consumer surplus if the price is a/2?

6.Marvin has a Cobb-Douglas utility function, U = q₁
^0.5q₂
^0.5, his income is Y = 100, and , initially he faces prices of p₁= 1 and p₂= 2. If p₁increases to 2, what are his CV,

CS, and EV?

7.Fangwen’s utility is U(q_1,q₂)_{= q₁+ q_2.The price of each good is $1, and her monthly income is $4,000. Her firm wants her to relocate to another city where the price of q₂is $2, but the price of q₁and her income remain constant. What would be her equivalent variation or compensating variation?}

HW3 1. Alex spends his money on food, a normal good, and all other goods (also normal). Decompose the total effect of a decrease in food prices into substitution effects and income effects. (i.e. draw the graph) 2. If Maria’s utility function is U = 2q10.5 + q2: a. What are her demand functions for the two goods? b. What are her income elasticity for the two goods? c. What are her Engel Curve for the two goods? 3. Bill’s utility function is U = 2ln(q1) + 2ln(q2). What is his compensated demand function for q1? 4. Siggi’s quasilinear utility function is U = 4ln(q1) + q2. His budget for these goods is Y = 10. Originally, the prices are p1 = p2 = 1. However, the price of the first good rises to p1 = 2. Discuss the substitution, income, and total effect on the demand for q1. 5. If the inverse demand function for radios is p = a – bq, what is the consumer surplus if the price is a/2? 6. Marvin has a Cobb-Douglas utility function, U = q10.5 q20.5, his income is Y = 100, and , initially he faces prices of p1 = 1 and p2 = 2. If p1 increases to 2, what are his CV, CS, and EV? 7. Fangwen’s utility is U(q1, q2) = q1 + q2. The price of each good is $1, and her monthly income is $4,000. Her firm wants her to relocate to another city where the price of q2 is $2, but the price of q1 and her income remain constant. What would be her equivalent variation or compensating variation?

hw-3-0yxycrud.docx

Komalavalli · Accepted Answer

Question 1
Let us Good X as Food and Good Y as other normal good. Initially the consumers faces equilibrium at point R with budget line PQ where Indifference curve I1 is tangent to the budget line.
Decrease in price of food (good X) pivots the budget line outward from PQ to PQ1 new equilibrium will be at T where new Indifference curve I2 tangent to PQ1. The movement from the R to H on the I1 is the substitution effect whereby the consumer increases his purchases of food from В to D by substituting food for Good Y because it is cheaper.
Return the withheld income to the customer such that it returns to the budget line PQ1 and is in equilibrium again at point T of the curve to isolate the income effect from the pricing effect. The income effect of a drop in the price of good X is represented by the movement of the point H on the indifference curve beneath the I1 curve to the point T above the high indifference curve I2. The actual income of consumers increases owing to a drop in the price of X, according to the compensation mechanism for the change in income.
Question 2:
U = 2q10.5+q2
Budget constraint I = P1q1+P2q2
MU1 = 2*0.5q1-0.5 = q1-0.5
MU2 = 1
MU1/P1 = MU2/P2
q1-0.

1.Alex spends his money on food, a normal good, and all other goods (also normal). Decompose the total effect of a decrease in food prices into substitution effects and income effects. (i.e. draw the...

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