Posted: March 18th, 2023

Marginal Rate of Substitution Research Paper


Marginal Rate of Substitution (MRS) is the rate that an individual is ready to give up from “good A” to obtain one or more unit of “good B” while keeping the overall utility constant. In other words, MRS reveals how many units of good x that an individual is ready to give up to gain extra unit of good y while keeping the same level of utility constant. The MRS involves the trade off of goods to change the allocation of the total bundles of goods while maintaining the level of satisfaction. Typically, MRS is calculated between goods being placed on indifferent curve. The product of cheeseburger and hotdogs is used to illustrate the MRS. If the marginal rate of substitution of cheeseburger for hot dogs is 2, thus, consumer will be willing to give 2 cheeseburger to obtain 1 extra hot dog.

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However, marginal rate of substitution diminishes as consumer substitutes one product for another. The law of marginal rate of substitution states that there is a decline in the MRS as an individual moves down on the standard convex-shaped curve. Typically, the MRS diminishes over time because it is subject to diminishing marginal utility. The more units of goods consumed the less additional satisfaction that each additional goods creates. In other words, the more an individual consumes a particular good, the more he will be willing to substitute the good. For example, an increase in the consumption of tea will lead to a decline in the marginal utility of coffee.

The data in the Table 1 are used to explain the reason marginal rate of substitution diminishes as a consumer substitute’s one product from another.

Table 1: Marginal Rate of Substitution


Good X

Good Y

MRS of X for Y















2: 1




1: 1

From the table 1, it is revealed that when a consumer moves from 4th to 5th combination, his or her the MRS of good X for good Y declines to one (1:1).


Price elasticity of demand measures the degree of responsiveness of the quantity of good demanded due to a change in price. In the other word, a price elasticity of demand reveals the proportionate change in quantity demanded due to a given proportionate change in price.

The formula to calculate the price elasticity of demand is as follows:

Ed = Percentage Change in Quantity Demanded

Percentage Change in Price

The paper uses the price elasticity of demand of nicotine product such as tobacco or cigarette to measure a price elasticity of demand of nicotine-addicted users, versus the group of “social smokers. Analysis of the price elasticity of demand between social smokers and additive smokers reveals that if the government increases the price of tobacco in order to decline the tobacco consumption in the society, the price elasticity of demand for tobacco will be more elastic for the social smokers than addictive smokers. Essentially, nicotine addicted users will be less price sensitive because they are already addicted to tobacco smoking and it would be very difficult for them to stop smoking. On the other hand, social smokers such as teenagers will record higher price elasticity for tobacco because they have not yet being addicted to tobacco smoking. Thus, they will be price sensitive to the increase in the price of tobacco.

Tobacco smoking is one of the major health problems globally and tobacco-smoking kill estimated 5 million people annually. However, millions of tobacco premature death could be prevented if governments can implement effective interventions to curb tobacco smoking, and several government policies are being implemented to drastically decline tobacco smoking. Some of the policies are as follows:

A ban on tobacco advertising,

Increase on excise tax on tobacco,

Increase on import duties on tobacco,

Intervention to reduce tobacco production

Despite the effort of government in declining the rate of tobacco smoking, the price intervention cannot reduce the smoking habit of addicted smokers; however, the price intervention can reduce the smoking habit of social smokers. (Jha, Chaloupka, Moore, et al. 2006).


Work full time and take course online:

Ranking is the most important attributes;

Ranking is twice important as price.

Ranking is three times important as location.

Quitting job and attends school full time:

location becomes three times as important as ranking;

Location is twice as important as price.













a. If Roshima wants to pursue her MBA education while keeping her full-time job, ranking will be the most important attribute. Thus, the expected utility (EU) for each school will be based on ranking is based on the following calculation of the expected utility of the two schools:

ASU Ranking:

= 80/100 = 80%

UOP Ranking = 70/100 = 70%

Thus, ASU’s ranking for EU is 10% greater than UOP ranking. Thus, Roshima should choose ASU as an option while keeping her full time job. Based on the results, Roshima should pursue her MBA program at the Arizona State University to maximize her expected utility.

b. If Roshima plans to quit her job and dedicate on her studies, thus, she should choose University of Phoenix to maximize her expected utility because location is given the highest priority and ranking is given the second priority.



Ranking =80

Total =130



Ranking =70

Total =140

Thus, Roshima should choose UOP to maximize her expected utility to study full time while quitting her job.

C. If the probability of being laid off and unable to find a new job is estimated at 0.6, Roshima should choose University of Phoenix to pursue her MBA program based on the calculation below.

ASU =130 x 0.6=78

UOP=140x 0.6=84.

Based on the results of the calculation, Roshima should choose the option of UOP if laid off from her job.

2 a. Price elasticity of demand of Bagels is as follows:

Px= — 40.73(0.85)

Px =-34.62

Quantity is as follows;

Qx = -15.87 — 40.73(0.85) + 84.17(0.79) + 0.55(216)

Qx =-15.87-34.62+66.49+118.8

Qx =-50.49+185.29

Qx =134.8

Price = — 40.73(0.85)

Price =-34.62

Price elasticity of demand= 134.8


Price elasticity of demand= -3.89

b. To derive an expression for the (inverse) demand curve for Einsteins’s Bagels then,


Qx = — 40.73 (0.85)


c. Qx =134.8

Cost of production =$0.10 per bagel

Cost of production=134.8 x $0.10

Cost of production of all bagels =134.8 x $0.10

Cost of production of all bagels =$13.48

Based on the results, the company should reduce price to sell more bagels and maximize the profit.

d. Yes, Einstein Bagels should spend more on advertising to attract the increase demand for bagels.


Jha, P. Chaloupka, F.J. Moore, J. et al. (2006). Chapter 46 Tobacco Addiction from the book Disease Control Priorities in Developing Countries. Second edition. World Bank.

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