A. Consider a consumer whose preferences can be represented by Cobb-Douglas utilityfunction u(x₁, x₂) = xx where ₁ and 2 are the quantities of good 1 and good 2she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote herincome.1. Derive the consumer's Marshallian demand functions.2. Derive the consumer's Hicksian demand functions.3. Derive the consumer's expenditure function.4. Let m = 20, P₁ = 2, and p2 = 1. Suppose that the price of good 1 drops to p₁ = 1.Find the following(a) Compensating variation (CV)(b) Equivalent variation (EV)(c) Change in consumer surplus (ACS)(d) Compare CV, ACS, and EV.5. Let m = 120, P₁ = 1, and p2 = 1. Suppose that the price of good 1 increases toP₁ = 2. Find the following(a) Compensating variation (CV)(b) Equivalent variation (EV)(c) Change in consumer surplus (ACS)(d) Compare CV, ACS, and EV. B. Albert works for a construction company. He has 70 hours a week available todivide between construction work and leisure, and he has no other sources of income.Albert is allowed to work as many hours (not exceeding 70) as he wishes to. His utilityfunction is U(c, r) = cr where c is his income spent on goods and r is the number ofhours of leisure that he has per week.• Suppose that the hourly wage is w dollars. Find Albert's demand for leisure as afunction of w. How many hours will Albert work at wage w?1• Albert is currently being paid $5 per hour. How many hours will he choose towork?• The company considers to raise Albert's hourly wage from $5 to $10. How manyhours will he choose to work at the new wage?• Assume now that the company offer "double pay" for overtime. That is, Albert ispaid $10 an hour for every hour beyond the amount he chose in part 2. Draw hisnew budget set and find the number of hours he will work under this new wagescheme.. Find the substitution and income effects on leisure if the hourly wage changes from$5 to $10.

Given Consumer utility function: u(x1,x2)=x113x223 .......(1) The price of good 1…

= A. Consider a consumer whose preferences can be represented by Cobb-Douglas utility function u(x1, x₂) = xx where ₁ and 2 are the quantities of good 1 and good 2 she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote her income. 1. Derive the consumer's Marshallian demand functions. 2. Derive the consumer's Hicksian demand functions. 3. Derive the consumer's expenditure function.

= A. Consider a consumer whose preferences can be represented by Cobb-Douglas utility function u(x1, x₂) = xx where ₁ and 2 are the quantities of good 1 and good 2 she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote her income. 1. Derive the consumer's Marshallian demand functions. 2. Derive the consumer's Hicksian demand functions. 3. Derive the consumer's expenditure function.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

A. Consider a consumer whose preferences can be represented by Cobb-Douglas utility
function u(x₁, x₂) = xx where ₁ and 2 are the quantities of good 1 and good 2
she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote her
income.
1. Derive the consumer's Marshallian demand functions.
2. Derive the consumer's Hicksian demand functions.
3. Derive the consumer's expenditure function.
4. Let m = 20, P₁ = 2, and p2 = 1. Suppose that the price of good 1 drops to p₁ = 1.
Find the following
(a) Compensating variation (CV)
(b) Equivalent variation (EV)
(c) Change in consumer surplus (ACS)
(d) Compare CV, ACS, and EV.
5. Let m = 120, P₁ = 1, and p2 = 1. Suppose that the price of good 1 increases to
P₁ = 2. Find the following
(a) Compensating variation (CV)
(b) Equivalent variation (EV)
(c) Change in consumer surplus (ACS)
(d) Compare CV, ACS, and EV.

B. Albert works for a construction company. He has 70 hours a week available to
divide between construction work and leisure, and he has no other sources of income.
Albert is allowed to work as many hours (not exceeding 70) as he wishes to. His utility
function is U(c, r) = cr where c is his income spent on goods and r is the number of
hours of leisure that he has per week.
• Suppose that the hourly wage is w dollars. Find Albert's demand for leisure as a
function of w. How many hours will Albert work at wage w?
1
• Albert is currently being paid $5 per hour. How many hours will he choose to
work?
• The company considers to raise Albert's hourly wage from $5 to $10. How many
hours will he choose to work at the new wage?
• Assume now that the company offer "double pay" for overtime. That is, Albert is
paid $10 an hour for every hour beyond the amount he chose in part 2. Draw his
new budget set and find the number of hours he will work under this new wage
scheme.
. Find the substitution and income effects on leisure if the hourly wage changes from
$5 to $10.

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Consider an individual with preferences represented by the following utility function: U (x1, 12) = x{x; The individual faces prices: P1 = 0.5; p2 = 1 And has income: M = 250 If the price of good one increases to p1 =1 For this change in price, mark all of the following answers that are correct. (EV = equivalent variation; CV = compensating variation) O In absolute value, EV is greater than Cv O In absolute values, change in Consumer surplus is smaller than CV. O In absolute value, CV is greater than EV In absolute values, change in Consumer Surplus is smaller than EV. There is not enough information to determine an answer.
8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…
Suppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of Y
A consumer has a (direct) utility function over x1 and x2: u(x₁, x2) = x₁x2.5 The price of good 1 is p1=1; the price of good 2 is p2=2; and the consumer has m=24 in income. Indicate which of the following statements is true. Select one: O Demand for good 1 is equal to 24. O Demand for good 2 is equal to 6. O Indirect utility function is equal to 32. O The consumer will demand 0 units of good 2. O None of the statements is correct.