Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 6, Problem 6.9P
a)
To determine
To prove:
Measurement of compensating variation due to increase in price.
b)
To determine
To prove:
Graphical representation of compensated demand curve.
c)
To determine
To prove:
Graphical representation of compensated demand curve due to change in price.
d)
To determine
To prove:
Whether there is a relation between the goods and welfare cost.
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For normal goodsA) the substitution effect of a price decrease will decrease the quantity of the good demanded while theincome effect of a price decrease will increase the quantity of the good demanded.B) the substitution and income effects of a price decrease will both increase the quantity of the gooddemanded.C) the substitution and income effects of a price decrease will both decrease the quantity of the gooddemanded.D) the substitution effect of a price decrease will increase the quantity of the good demanded while theincome effect of a price decrease will decrease the quantity of the good demanded.
A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1.
Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.
Units of
the Good
0
1
5678AWN2
3
4
Total Utility Total Utility
of X
of Y
0
0
620
1740
1120
3030
1500
3960
1820
4710
2080
5280
2300
5730
2460
6060
2580
6300
For the next 3 questions, assume that an individual consumes two goods X and Y.
The total utility (assumed measurable) of each good is independent of the rate of consumption of other goods.
The prices of X and Y are, respectively, $20 and $30.
If the consumer buys the fourth unit of X the Marginal Utility per Dollar Spent on X is 16 I
If the consumer has $210 to spend on X and Y, the utility-maximizing bundle is
The minimum budget necessary to move to a higher equilibrium consumption of X and Y is $
unit(s) of X and
unit(s) of Y.
Chapter 6 Solutions
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- Praxilla, who lived in ancient Greece, derives utility from reading poems and from eating cucumbers. Praxilla gets 30 units of marginal utility from her first poem 27 units of marginal utility from her second poem 24 units of marginal utility from her third poem, and so on, with marginal utility declining by three units for each additional poem. Praxilla gets six units of marginal utility for each of her next three cucumbers consumed, five units of marginal utility for each of her next three cucumbers consumed, four units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by one for every three cucumber consumed. A poem costs three bronze coins hut a cucumber costs only one bronze coin. Praxilla has 18 bronze coins. Sketch Praxillas budget set between poems and cucumbers, placing poems on the vertical axis and cucumbers on the horizontal axis. Start off with the choice of zero poems and 18 cucumbers, and calculate the changes in marginal utility of moving along the budget line to the next choice of one poem and 15 cucumbers. Using this step-by-step process based on marginal utility, create a table and identify Praxillas utility—maximizing choice. Compare the marginal utility of the two goods and the relative prices at the optimal choice to see if the expected relationship holds. Hint: Label the table columns: 1) Choice, 2} Marginal Gain from More Poems, 3) Marginal Loss from Fewer Cucumbers, 4) Overall Gain or Loss, 5) Is the previous choice Optimal? Label the table rows: 1) 0 Poems and 18 Cucumbers, 2) 1 Poem and 15 cucumbers, 3) 2 Poems and 12 cucumbers, 4) 3 Poems and 9 Cucumbers, 5) 4 Poems and 6 cucumbers 6) 5 Poems and 3 Cucumbers, 7) 6 Poems and 0 Cucumbers.arrow_forward. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible theywould choose to consume some of both commodities when their income is I but would choose toconsume only x when their income is I’ > I. (Remember: if you can draw it without violating anyof the basic assumptions on preferences, it could happen.)arrow_forwardExplain the difference between a positive and a negative network externality. A network externality for a good is positive if O A. the substitution effect of a price change is larger than the income effect, but a network externality is negative if the income effect is larger than the substitution effect. B. consumption by others decreases a typical consumer's marginal utility from consuming the good, but a network extemality is negative if consumption by others increases a typical consumer's marginal utility from the good. c. the price is lower the more people own it, but a network externality is negative if the price is lower the fewer people own it. D. the quantity demanded is higher the more people own it, but a network externality is negative if the quantity demanded is lower the more people own it. O E. it has a complement, but a network effect is negative if it has a substitute. Give an example of each. An example of a positive network externality is the dermand for A. a work of…arrow_forward
- ceriuppose that Isaiah has a weekly fixed budget and spends it all on haircuts and ice cream. At his current combination arof consumption, the marginal utility of the last dollar spent on haircuts is greater than the marginal utility of the last dollar spent on ice cream. Has Isaiah maximized his utility? A C E Yes, because changing his current consumption combination will reduce his total utility B No, because he can increase his total utility by purchasing more haircuts and D fewer ice creams Yes, because he has purchased 2 goods in proportion so that he can get- the maximum utility from each Yes, because he purchased the maximum possible with a limited budget No, because he can increase his total utility by purchasing fewer haircuts and more ice creamsarrow_forwardThe following gives the marginal utility of John’s consumption of three goods A, B and C.Unit of consumption MUaMUbMUc1202545218203031615244141018512815610612 Goods A, Band C costs ksh2, ksh1 and ksh3 respectively. How many units of each good should a consumer take to maximize utility with an income of ksh12arrow_forwardPeter har this utility function リ=x,° 0,5 0,5 メー Where U is utility and x, and x, and the volume of goods 1 og 2 Peters income can be expressed as m, while the price on the goods 1 and 2 is given by p, and p, When the price on good 1 is 2 dollar, and the price on good 2 is 1 dollars. Peter has a budgett of 200 dollars. Peter will buy XXX of good 1, and XXX of good 2 Calculate XXX and XXXarrow_forward
- Intialy mr. John is at equilibrium such that the last dollar spent on each of several products gives hi identical marginal utility i.e MUorange/porange=MUApple/pApple=...=MUn/pn where Mu orange =aditional utility derived from consuming one more unit of Apple ,pApple=price of a unit of Apple etc Q.how will Mr.Jhon react if the price of orange and other goods remain constant?and how can the equilibrium be restored?arrow_forwardIf we observe that a consumerâ s budget constraint has shifted inward, we can assume that the consumer will buy O fewer normal goods and fewer inferior goods O more normal goods and more inferior goods O fewer normal goods and more inferior goods more normal goods and fewer inferior goodsarrow_forwardIf we have money, we buy goods and services to satisfy our needs. In economics, thesatisfaction that we get from the consumption of goods and services is called utility. Usea utility graph to explain what happen to the utility when you keep on increasing thenumber of units consumed. Also explain what happens to the utility when you keep onincreasing the number of units consumed. Also explain what happens to the additionalutility (i.e. additional satisfaction) when you increase your consumption by one unitarrow_forward
- 10. Deriving demand from an indiference map Frances recently moved to San Diego, where they developed a taste for drinking Americanos and eating danishes. Assume throughout this problem that the price of an Americano is held constant at $3. On the following graph, the purple curves (I and I₂) describe two of Frances's indifference curves. The lines BC, and BC, represent bro budget constraints. Points X and Y show Frances's optimal consumption bundles subject to the budget constraints. AMERICANOS R2Xpe 16 14 DANISHES 12 14 ON 18 AK 20 Given the preceding graph and knowing the price of an Americano is $3, Frances's available income for Americanos and danahes isarrow_forward17) A ssume a consumer has $40 to spend and for both products the marginal utilities are shown in the following table: Quantity MU MU 1 35 80 2 20 40 3 12 18 Assume that each product sells for $10 per unit. a) How many units of each product will the consumer purchase? b) Assume the price of product B rises to $20 per unit. How will this consumer allocate her budget now? c) If the prices of both products rise to $20 per unit, what will be the budget allocation?arrow_forwardstion 51 The following marginal utility data is for products X and Y. Assume that the prices of x and Y are 54 and $2 respectively and that the consumer's income is $18 wet ered d out of Units Marginal Units Marginal utility, Y of X utility, X of Y ove fiag 20 16 2 16 2. 14 3 12 3 12 4 8. 4 10 5. 8. 6 4. 6 Which of the following shows the price and quantity demanded of X? (A) (B) (C) (D) Qd P Qd Qd Qd P. $4 $4 2 $4 3 $4 3. 2 5. 2. 4 2 9. Select one: O a. column (B) O b. column (A) O c. column (C) O d. column (D)arrow_forward
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