Question

You must show your work on all mathematical questions and I must be able to follow your steps.

The institutional research office has recently conducted a survey group of consumers. According to demographic data, the research office has given you the following:

                        Typical weekly consumer income                    $500

                        Price of Frosty Cola                                        $2.50 per case

                        Price of Coca-Cola                                         $5.00 per case

You want to break this data down for the chief financial officer in two forms: a slope- intercept equation for the typical consumer’s budget constraint and a graphical analysis showing him the typical consumer’s budget set.The CFO has specifically asked for Frosty Cola to be the good on the vertical axis.

  a) Put the equation for the budget constraint in slope-intercept form.

b) Illustrate the typical consumer’s budget set (again, place quantity of Frosty Cola on the vertical axis).

c) The CFO asks you if the price of Frosty Cola were to increase by $2.50 per case, what would happen to the budget constraint? Illustrate and explain.

d) Lastly, the CFO asks you that if the typical consumer wished to purchase four cases of Coca- Cola, how much Frosty Cola could that individual purchase? Calculate and show using the slope-intercept equation from part a). Assume the original price of Frosty Cola and the original budget constraint.

Answer 1

a) Based on the consumer survey, the typical weekly consumer income has been estimated to be $500 and the respective prices of Frosty-Cola and Coca Cola are $2.50 per case and $5 per case. Therefore, the equation form budget line or constraint can be expressed as 2.50F+5C=500 where F and C represent the number of cases of Frosty-Cola and Coca-Cola respectively. The intercept of the Frosty Cola in this case=$500/$2.50=200 and the intercept of the Coca-Cola=$500/$5=100. The slope of the budget constraint in this case=-$2.50/$5=-0.5

Therefore, the standard slope-intercept for the budget constraint with respect to Frost-Cola can be written as:-

F=200-0.5C or C=100-0.5F

b) Figure-1 in the document attached below represents the budget constraint of an individual based on the demographic data obtained from the consumer survey. The vertical axis represents the quantity or number of Frosty Cola or F and the horizontal axis denotes the quantity or number of Coca-Cola or C. The consumer budget constraint is denoted as BC1. The intercept of the Frosty-Cola or F is 200 indicating that given the weekly income and the per case price of F or P(F) if the consumer spends his entire weekly income on the consumption of frosty-cola and does not buy any coca-cola or C then he or she would be able to purchase 200 cases of F. Now, alternatively, if the consumer spends his or her entire income on the consumption of C and does not buy any F, then he or she would be able to buy 100 cases of C which is the intercept of C as indicated in the graph.

c) Now, if the price of F increases by $2.50 per case, the price of F or P(F) would now become=($5+$2.50)=$7.50 per case. The per-case price of C and the weekly consumer income remain the same. Therefore, now the intercept of F would become=$500/$7.50=66.66 approximately and the intercept of C would remain the same as P(C) has remained unchanged. The slope of the budget constraint would now become=-$2.50/$7.50=-0.33 approximately. Figure-2 in one of the document attached below depicts the impact of an increase in P(F) or per-case price increase of F on the consumer budget constraint. Due to the increase in P(F), the intercept of F decreases from 200 to 66.66 and the consumer moves from BC1 to BC2, considering the weekly income of the consumer and the intercept of C as constant as the P(C) and consumer weekly income both have remained unchanged.

d) The slope-intercept form of budget constraint with respect to F has been derived as C=100-0.5F in part a). Now, the consumer wish to buy 4 cases of C or C=4.

Hence, plugging the desired or preferred value of C by the consumer into the slope-intercept form with respect to C, we can obtain:-

C=100-0.5F

4=100-0.5F

0.5F=100-4

0.5F=96

F=96/0.5

F=192

Therefore, given the weekly consumer income and P(F) and P(C), if the consumer chooses to buy 4 C then he or she would purchase 192 cases of Frosty Cola or F.