Refer to Guidance.

QSTION ONE
TAXATION VERSUS SUPPLY AND DEMAND ELASTICITY
In inelastic good market, change in price does not cause any change in the consumption, for elastic goods changes in prices trigger great changes in the consumption patterns.
An imposition of exercise tax by the government increases the levels of prices for the target good. The change in the quantity supplied and demanded depends on the elasticity on the both sides of supply and demand. For goods whose both supply and demand elasticity are elastic, little revenue can be gained since the buyer and consumers can alter their expenditures and supplies on the goods whose price has been increased by the taxes.
In a case where the demand is inelastic and supply elastic only suppliers have a choice of changing their expenditure patterns and thus the tax imposition lies its burden heavily on consumers and not the producers. The producers can alter the level of production (supply level) to suit the market equilibrium. Consumers have no choice since they are addicted to the products thus little or no change in the consumption pattern once the tax is imposed. In this case a tax imposition or an increase in the rate of exercise tax will yield higher revenue compared to a case of elastic goods though the tax burden is heavily laid on the consumers
A case where both supply and demand are inelastic reaps of higher amount of revenue to the government once a tax is imposed. In this case tax burden is equally laid on producers and consumers for no one have an option to its choices on either production patterns or consumption patterns.
Elastic, X(GUNS) goods Market equilibrium
Y-AXIS
DD
SS
DDDDDDD
-AXIS
PE
P
QE X-AXIS
QUANTITY
When tax is imposed on the goods whose market equilibrium is indicated above the price changes from PE to a higher point say p1. Once this happened, the supply curve shifts backward for adjustments which alter the market equilibrium quantity from QE to a point back though along the consumption curve. In this case tax burden is equally laid on both consumers and producers.
Market equilibrium for BUTTER, good Y, Inelastic demand
D Y -axis
SSSSSS
PE
Price (P)
DOrigin
Quantity (Q) QE X-axis
D denotes the demand curve
S supply curve
QE equilibrium Quantity
PE equilibrium price
Imposition of exercise tax will shift PE to a higher level
Tax imposition on butter will highly hurt consumers since the change it increases the prices and they cannot alter the quantity they demand. Only the suppliers can alter the quantity the supply, but that’s impossible since the quantity demanded has not changed.
As a consequence the tax imposition on guns would suit the government whose aim is not necessarily tax collection but cares on hurting the consumers (voters).
QUESTION TWO
A] CONSUMER PREFERENCES ON GOODS X and Y GIVEN THAT P(X) =P(Y), p(X) =price of x and p(Y) price of good Y.
UTILITY FUNCTION, U (X,Y)=(X2+Y2).5
Utility function given describes a situation in which a bundle of X and Y goods have unit share of consumption. That is the consumer consumes one the same number of units at a given level of income (budget constraint).
We trace whether the consumer preference for good X and Y satisfy the three axioms of consumer preference in utility. I) axiom of order or completeness- the utility function incorporates goods X and Y and thus it fulfills the axiom of completeness. Too, the consumer preference dictates for the choice of the most complete bundle- that for the two goods no good is left out. Ii) Axiom of transitivity the utility preference directs on the choice preferred by the customer that the higher level of utility indicate a better position for the consumer. Iii) Invariant transitivity from the consumer utility function for X and Y it is indicated that more bundles of X and Y can not provide a lesser utility. That is if there is an increase in the number of y and x then utility increases respectively.
Therefore, the consumer preferences fulfill the three axioms of consumer preferences.
Do the consumer preferences fulfill the decreasing marginal rate of substitution?
Along the utility curve the marginal utility is always zero. I.e. the sum of partial derivatives of the utility is always zero. Therefore, using different points along the utility curve, we can construct a marginal rate of substitution curve. Whenever the consumer consumes more of y then for the utility to hold he/she consumes less of x and the same occurs whenever he/she consumes more of x, less of y. thus marginal rate of substitution occurs due diminishing marginal utility for consumption of more goods.
Good y
Utility function
[bookmark: _GoBack] Good x,
We trace whether the consumer preference for good X and Y satisfy the three axioms of consumer preference in utility. I) axiom of order or completeness- the utility function incorporates goods X and Y and thus it fulfills the axiom of completeness. Too, the consumer preference dictates for the choice of the most complete bundle- that for the two goods no good is left out. Ii) Axiom of transitivity the utility preference directs on the choice preferred by the customer that the higher level of utility indicate a better position for the consumer. Iii) Invariant transitivity from the consumer utility function for X and Y it is indicated that more bundles of X and Y can not provide a lesser utility. That is if there is an increase in the number of y and x then utility increases respectively.
Therefore, the consumer preferences fulfill the three axioms of consumer preferences.
Do the consumer preferences fulfill the decreasing marginal rate of substitution?
Along the utility curve the marginal utility is always zero. I.e. the sum of partial derivatives of the utility is always zero. Therefore, using different points along the utility curve, we can construct a marginal rate of substitution curve. Whenever the consumer consumes more of y then for the utility to hold he/she consumes less of x and the same occurs whenever he/she consumes more of x, less of y. thus marginal rate of substitution occurs due diminishing marginal utility for consumption of more goods.
We trace whether the consumer preference for good X and Y satisfy the three axioms of consumer preference in utility. I) axiom of order or completeness- the utility function incorporates goods X and Y and thus it fulfills the axiom of completeness. Too, the consumer preference dictates for the choice of the most complete bundle- that for the two goods no good is left out. Ii) Axiom of transitivity the utility preference directs on the choice preferred by the customer that the higher level of utility indicate a better position for the consumer. Iii) Invariant transitivity from the consumer utility function for X and Y it is indicated that more bundles of X and Y can not provide a lesser utility. That is if there is an increase in the number of y and x then utility increases respectively.
Therefore, the consumer preferences fulfill the three axioms of consumer preferences.
Do the consumer preferences fulfill the decreasing marginal rate of substitution?
Along the utility curve the marginal utility is always zero. I.e. the sum of partial derivatives of the utility is always zero. Therefore, using different points along the utility curve, we can construct a marginal rate of substitution curve. Whenever the consumer consumes more of y then for the utility to hold he/she consumes less of x and the same occurs whenever he/she consumes more of x, less of y. thus marginal rate of substitution occurs due diminishing marginal utility for consumption of more goods.