ECON3102-005Chapter 4: Consumer and Firm

Behavior

Neha Bairoliya

Spring 2014

Representative Consumer

• The representative consumer values two goods: leisure l and theconsumption good c .

• Consumer’s preferences Consumers preferences over consumptionand leisure as represented by indifference curves. The preferencescan be captured by the utility function U(c , l).

• A particular combination (c , l) of c and l is called a consumptionbundle.

Representative Consumer

• The representative consumer values two goods: leisure l and theconsumption good c .

• Consumer’s preferences Consumers preferences over consumptionand leisure as represented by indifference curves. The preferencescan be captured by the utility function U(c , l).

• A particular combination (c , l) of c and l is called a consumptionbundle.

Representative Consumer

• The representative consumer values two goods: leisure l and theconsumption good c .

• Consumer’s preferences Consumers preferences over consumptionand leisure as represented by indifference curves. The preferencescan be captured by the utility function U(c , l).

• A particular combination (c , l) of c and l is called a consumptionbundle.

The Representative Consumer’s Preferences

• If U(c1, l1) > U(c2, l2), then the consumer strictly prefers bundle(c1, l1) to bundle (c2, l2).

• If U(c1, l1) < U(c2, l2), then the consumer strictly prefers bundle(c2, l2) to bundle (c1, l1).

• If U(c1, l1) = U(c2, l2), then the consumer is indifferent between thetwo bundles.

• In fact, the actual level of utility is irrelevant. What matters is theorder of preferences implied by the utility function.

The Representative Consumer’s Preferences

• If U(c1, l1) > U(c2, l2), then the consumer strictly prefers bundle(c1, l1) to bundle (c2, l2).

• If U(c1, l1) < U(c2, l2), then the consumer strictly prefers bundle(c2, l2) to bundle (c1, l1).

• If U(c1, l1) = U(c2, l2), then the consumer is indifferent between thetwo bundles.

• In fact, the actual level of utility is irrelevant. What matters is theorder of preferences implied by the utility function.

The Representative Consumer’s Preferences

• If U(c1, l1) > U(c2, l2), then the consumer strictly prefers bundle(c1, l1) to bundle (c2, l2).

• If U(c1, l1) < U(c2, l2), then the consumer strictly prefers bundle(c2, l2) to bundle (c1, l1).

• If U(c1, l1) = U(c2, l2), then the consumer is indifferent between thetwo bundles.

• In fact, the actual level of utility is irrelevant. What matters is theorder of preferences implied by the utility function.

The Representative Consumer’s Preferences

• If U(c1, l1) > U(c2, l2), then the consumer strictly prefers bundle(c1, l1) to bundle (c2, l2).

• If U(c1, l1) < U(c2, l2), then the consumer strictly prefers bundle(c2, l2) to bundle (c1, l1).

• If U(c1, l1) = U(c2, l2), then the consumer is indifferent between thetwo bundles.

• In fact, the actual level of utility is irrelevant. What matters is theorder of preferences implied by the utility function.

Assumptions on The RepresentativeConsumer’s Preferences

• More is always preferred to less: the consumer always likes moreleisure, and more consumption.

• The consumer likes diversity, i.e. he prefers mixtures to extremes:He would rather have some consumption and some leisure ratherthan a lot of leisure and no consumption!

• Consumption and leisure are normal goods to the consumer (asopposed to inferior goods!): he consumes more of each as hisincome goes up.

Assumptions on The RepresentativeConsumer’s Preferences

• More is always preferred to less: the consumer always likes moreleisure, and more consumption.

• The consumer likes diversity, i.e. he prefers mixtures to extremes:He would rather have some consumption and some leisure ratherthan a lot of leisure and no consumption!

• Consumption and leisure are normal goods to the consumer (asopposed to inferior goods!): he consumes more of each as hisincome goes up.

Assumptions on The RepresentativeConsumer’s Preferences

• More is always preferred to less: the consumer always likes moreleisure, and more consumption.

• The consumer likes diversity, i.e. he prefers mixtures to extremes:He would rather have some consumption and some leisure ratherthan a lot of leisure and no consumption!

• Consumption and leisure are normal goods to the consumer (asopposed to inferior goods!): he consumes more of each as hisincome goes up.

Indifference Curves (IC curves)

DefinitionAn indifference curve connects a set of points that represent bundlesamong which the consumer is indifferent.

• IC curves are downward sloping (more is preferred to less).

• convex or bowed-in toward the origin (consumer’s preferences fordiversity).

Indifference Curves (IC curves)

DefinitionAn indifference curve connects a set of points that represent bundlesamong which the consumer is indifferent.

• IC curves are downward sloping (more is preferred to less).

• convex or bowed-in toward the origin (consumer’s preferences fordiversity).

Indifference Curves

Indifference CurvesDefinitionThe marginal rate of substitution of leisure for consumption, denotedMRSlc , is the rate at which the consumer is just willing to substituteleisure for consumption goods.

• Between bundles A and B, the rate atwhich the consumer substitutes c for lis c1−c2

l1−l2= - the slope of line AB.

• This is because if you take away(c1 − c2) from him, he would ask to begiven (l2 − l1) in return, in order toremain indifferent between bundles Aand B.

• As bundle B gets arbitrarily close tobundle A, this rate of substitutionbecomes ∂c

∂l = - the slope of the linetangent to the IC at point A (thederivative of IC at A).

Indifference CurvesDefinitionThe marginal rate of substitution of leisure for consumption, denotedMRSlc , is the rate at which the consumer is just willing to substituteleisure for consumption goods.

• Between bundles A and B, the rate atwhich the consumer substitutes c for lis c1−c2

l1−l2= - the slope of line AB.

• This is because if you take away(c1 − c2) from him, he would ask to begiven (l2 − l1) in return, in order toremain indifferent between bundles Aand B.

• As bundle B gets arbitrarily close tobundle A, this rate of substitutionbecomes ∂c

∂l = - the slope of the linetangent to the IC at point A (thederivative of IC at A).

Indifference CurvesDefinitionThe marginal rate of substitution of leisure for consumption, denotedMRSlc , is the rate at which the consumer is just willing to substituteleisure for consumption goods.

• Between bundles A and B, the rate atwhich the consumer substitutes c for lis c1−c2

l1−l2= - the slope of line AB.

• This is because if you take away(c1 − c2) from him, he would ask to begiven (l2 − l1) in return, in order toremain indifferent between bundles Aand B.

• As bundle B gets arbitrarily close tobundle A, this rate of substitutionbecomes ∂c

∂l = - the slope of the linetangent to the IC at point A (thederivative of IC at A).

Indifference CurvesDefinitionThe marginal rate of substitution of leisure for consumption, denotedMRSlc , is the rate at which the consumer is just willing to substituteleisure for consumption goods.

• Between bundles A and B, the rate atwhich the consumer substitutes c for lis c1−c2

l1−l2= - the slope of line AB.

• This is because if you take away(c1 − c2) from him, he would ask to begiven (l2 − l1) in return, in order toremain indifferent between bundles Aand B.

• As bundle B gets arbitrarily close tobundle A, this rate of substitutionbecomes ∂c

∂l = - the slope of the linetangent to the IC at point A (thederivative of IC at A).

Indifference Curves

MRSl,c = - the slope of the IC passing through bundle (c , l):

Consumer’s Time Constraint

• Each period, the consumer has h units of hours of time available, toallocate between l units of leisure and Ns units of work.

• The time constraint isl + Ns = h

Consumer’s Time Constraint

• Each period, the consumer has h units of hours of time available, toallocate between l units of leisure and Ns units of work.

• The time constraint isl + Ns = h

The Consumer’s Real Disposable Income

• The numeraire throughout is the consumption good. That is, allprices will be in terms of units of consumption (i.e., in real terms).

• The consumer receives real wage w per hour, so real wage incomewNs . She pays lump-sum taxes T to the government.

• He receives π units of current consumption as in the form ofdividend income from the firm.

• Hence, his disposable income is:

wNs + π − T

The Consumer’s Real Disposable Income

• The numeraire throughout is the consumption good. That is, allprices will be in terms of units of consumption (i.e., in real terms).

• The consumer receives real wage w per hour, so real wage incomewNs . She pays lump-sum taxes T to the government.

• He receives π units of current consumption as in the form ofdividend income from the firm.

• Hence, his disposable income is:

wNs + π − T

The Consumer’s Real Disposable Income

• The numeraire throughout is the consumption good. That is, allprices will be in terms of units of consumption (i.e., in real terms).

• The consumer receives real wage w per hour, so real wage incomewNs . She pays lump-sum taxes T to the government.

• He receives π units of current consumption as in the form ofdividend income from the firm.

• Hence, his disposable income is:

wNs + π − T

The Consumer’s Real Disposable Income

• The numeraire throughout is the consumption good. That is, allprices will be in terms of units of consumption (i.e., in real terms).

• The consumer receives real wage w per hour, so real wage incomewNs . She pays lump-sum taxes T to the government.

• He receives π units of current consumption as in the form ofdividend income from the firm.

• Hence, his disposable income is:

wNs + π − T

Consumer’s Budget Constraint

• The consumer’s budget constraint (BC) is:

c = wNs + π − T

• substituting the time constraint gives:

c = w(h − l) + π − T

• or,c + wl︸ ︷︷ ︸

Implicit expenditure on goods

= wh + π − T︸ ︷︷ ︸Implicit Real Disposable Income

• w is interpreted as the opportunity cost of leisure.

Consumer’s Budget Constraint

• The consumer’s budget constraint (BC) is:

c = wNs + π − T

• substituting the time constraint gives:

c = w(h − l) + π − T

• or,c + wl︸ ︷︷ ︸

Implicit expenditure on goods

= wh + π − T︸ ︷︷ ︸Implicit Real Disposable Income

• w is interpreted as the opportunity cost of leisure.

Consumer’s Budget Constraint

• The consumer’s budget constraint (BC) is:

c = wNs + π − T

• substituting the time constraint gives:

c = w(h − l) + π − T

• or,c + wl︸ ︷︷ ︸

Implicit expenditure on goods

= wh + π − T︸ ︷︷ ︸Implicit Real Disposable Income

• w is interpreted as the opportunity cost of leisure.

Consumer’s Budget Constraint

For convenience, we rewrite the BC as: c = −wl + wh + π − T

The Consumer’s Budget Constraintif T > π

The Consumer’s Budget Constraintif T < π

Consumer’s Budget Constraint

Just to show that either case is easy to analyze and that the implicationsdo not change, we will assume in this chapter that T < π. That is, wewill be working with the kinked budget constraint.

Consumer Optimization

DefinitionThe optimal consumption bundle (OCB) is the point representing aconsumption-leisure pair that is on the highest possible indifference cureand is on or inside the budget constraint.

• We next show that the OCB is the point where the IC is tangent tothe budget constraint.

Consumer Optimization

DefinitionThe optimal consumption bundle (OCB) is the point representing aconsumption-leisure pair that is on the highest possible indifference cureand is on or inside the budget constraint.

• We next show that the OCB is the point where the IC is tangent tothe budget constraint.

Consumer Optimization

• First the consumer will never chose apoint inside the budget constraint, sowe know the OCB is on line (AB).

• At point F, -slope of IC (MRSl,c) >-slope of the budget constraint (=w) :MRSl,c > w ).

• Hence, at point F, rate at which theconsumer would trade leisure forconsumption > the rate at which hecan trade leisure for consumption.

• the consumer would then be better offif he sacrifices consumption for moreleisure.

Consumer Optimization

• First the consumer will never chose apoint inside the budget constraint, sowe know the OCB is on line (AB).

• At point F, -slope of IC (MRSl,c) >-slope of the budget constraint (=w) :MRSl,c > w ).

• Hence, at point F, rate at which theconsumer would trade leisure forconsumption > the rate at which hecan trade leisure for consumption.

• the consumer would then be better offif he sacrifices consumption for moreleisure.

Consumer Optimization

• First the consumer will never chose apoint inside the budget constraint, sowe know the OCB is on line (AB).

• At point F, -slope of IC (MRSl,c) >-slope of the budget constraint (=w) :MRSl,c > w ).

• Hence, at point F, rate at which theconsumer would trade leisure forconsumption > the rate at which hecan trade leisure for consumption.

• the consumer would then be better offif he sacrifices consumption for moreleisure.

Consumer Optimization

• First the consumer will never chose apoint inside the budget constraint, sowe know the OCB is on line (AB).

• At point F, -slope of IC (MRSl,c) >-slope of the budget constraint (=w) :MRSl,c > w ).

• Hence, at point F, rate at which theconsumer would trade leisure forconsumption > the rate at which hecan trade leisure for consumption.

• the consumer would then be better offif he sacrifices consumption for moreleisure.

Consumer Optimization

• At point E, -slope of IC (MRSl,c) <-slope of the budget constraint (=w) :MRSl,c < w ).

• Hence, the consumer would then bebetter off sacrificing leisure for moreconsumption. So, E is not the OCB.

• Hence, the OCB is the point were:MRSl,c = w : where the rate at whichthe consumer would trade consumptionfor leisure= price of leisure in units ofconsumption.

Consumer Optimization

• At point E, -slope of IC (MRSl,c) <-slope of the budget constraint (=w) :MRSl,c < w ).

• Hence, the consumer would then bebetter off sacrificing leisure for moreconsumption. So, E is not the OCB.

• Hence, the OCB is the point were:MRSl,c = w : where the rate at whichthe consumer would trade consumptionfor leisure= price of leisure in units ofconsumption.

Consumer Optimization

• At point E, -slope of IC (MRSl,c) <-slope of the budget constraint (=w) :MRSl,c < w ).

• Hence, the consumer would then bebetter off sacrificing leisure for moreconsumption. So, E is not the OCB.

• Hence, the OCB is the point were:MRSl,c = w : where the rate at whichthe consumer would trade consumptionfor leisure= price of leisure in units ofconsumption.

An Increase in π − T for the Consumer (w isconstant.)

• Real dividends or taxes change for theconsumer:

• Note the c and l are normal goods.

• An increase in dividends or a decreasein taxes will then cause the consumerto increase consumption and reducethe quantity of labor supplied (increaseleisure).

An Increase in π − T for the Consumer (w isconstant.)

• Real dividends or taxes change for theconsumer:

• Note the c and l are normal goods.

• An increase in dividends or a decreasein taxes will then cause the consumerto increase consumption and reducethe quantity of labor supplied (increaseleisure).

An Increase in π − T for the Consumer (w isconstant.)

• Real dividends or taxes change for theconsumer:

• Note the c and l are normal goods.

• An increase in dividends or a decreasein taxes will then cause the consumerto increase consumption and reducethe quantity of labor supplied (increaseleisure).

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

Breaking Down the Income and SubstitutionEffects

• Because of the increase in w, thebudget constraint pivots around pointB (from AB to EB).

• Given the new higher w , suppose wetake away disposable income from him(example from π) until he is indifferentbetween his new OCB (point O) andhis original OCB (point F).

• Concretely, we force the consumer toface fictive budget constraint (JKD).The movement from F to O is thesubstitution effect:

• As w increases, leisure becomesrelatively more expensive and theconsumer substitutes away from it.

Breaking Down the Income and SubstitutionEffects

• Because of the increase in w, thebudget constraint pivots around pointB (from AB to EB).

• Given the new higher w , suppose wetake away disposable income from him(example from π) until he is indifferentbetween his new OCB (point O) andhis original OCB (point F).

• Concretely, we force the consumer toface fictive budget constraint (JKD).The movement from F to O is thesubstitution effect:

• As w increases, leisure becomesrelatively more expensive and theconsumer substitutes away from it.

Breaking Down the Income and SubstitutionEffects

• Because of the increase in w, thebudget constraint pivots around pointB (from AB to EB).

• Given the new higher w , suppose wetake away disposable income from him(example from π) until he is indifferentbetween his new OCB (point O) andhis original OCB (point F).

• Concretely, we force the consumer toface fictive budget constraint (JKD).The movement from F to O is thesubstitution effect:

• As w increases, leisure becomesrelatively more expensive and theconsumer substitutes away from it.

Breaking Down the Income and SubstitutionEffects

• Because of the increase in w, thebudget constraint pivots around pointB (from AB to EB).

• Given the new higher w , suppose wetake away disposable income from him(example from π) until he is indifferentbetween his new OCB (point O) andhis original OCB (point F).

• Concretely, we force the consumer toface fictive budget constraint (JKD).The movement from F to O is thesubstitution effect:

• As w increases, leisure becomesrelatively more expensive and theconsumer substitutes away from it.

Breaking Down the Income and SubstitutionEffects

• The movement from O to H is a pureincome effect.

• For the income effect, suppose w staysthe same, but non-wage incomeincreases so that the budget constraintshifts in a parallel way from (JKD) toEBD.

• Because both goods are normal, theconsumer consumes more of both.

Breaking Down the Income and SubstitutionEffects

• The movement from O to H is a pureincome effect.

• For the income effect, suppose w staysthe same, but non-wage incomeincreases so that the budget constraintshifts in a parallel way from (JKD) toEBD.

• Because both goods are normal, theconsumer consumes more of both.

Breaking Down the Income and SubstitutionEffects

• The movement from O to H is a pureincome effect.

• For the income effect, suppose w staysthe same, but non-wage incomeincreases so that the budget constraintshifts in a parallel way from (JKD) toEBD.

• Because both goods are normal, theconsumer consumes more of both.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

An Increase in the Market Real Wage Rate

• This has income and substitutioneffects.

• Substitution effect: the price of leisurerises, so the consumer substitutes fromleisure to consumption.

• Income effect: the consumer iseffectively more wealthy and, sinceboth goods are normal, consumptionincreases and leisure increases.

• Conclusion: Consumption must rise,but leisure may rise or fall.

Labor Supply Curve

• We assume that the substitution effectdominates so that as w increases, theconsumer consumes less leisure andhence works more.

Labor Supply Curve: Effect of an Increase inDividend Income or a Decrease in Taxes