Question

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                  $800

                        Price of Frosty Cola                                        $10.00 per case

                        Price of Coca-Cola                                          $20.00 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 the price of Frosty Cola to be the good on the vertical axis. (Round any quantity to the nearest whole unit in each part, if necessary.)        

(Please show work)

a) Derive the equation for the budget constraint in slope-intercept form. (6 points)

b) Illustrate and explain the typical consumer’s budget set (again, place quantity of Frosty Cola on the vertical axis). (5 points)

c) The CFO asks you if the price of Frosty Cola were to decrease to $5.00 per case, what would happen to the budget constraint? Illustrate and explain. (5 points)

d) Lastly, the CFO asks you that if the typical consumer wished to purchase seven cases of Coca-Cola, how much Frosty Cola could that individual purchase? Calculate and show.         Assume the original data. (4 points)

Answer 1

Ansa.) Price of frost cola (P_FC) = $10

Price of coca cola (P_CC)= $20

Income (I) = $800

I= P_FC × (FC)  + P_CC × ( CC) ..... eq(1)

The equation in the form of slope intercept is as follows:

FC = I/P_FC - (P_CC/P_FC) CC

In the slope intercept form, one is able to find the quantity of each good that an individual can purchase with given income, keeping the quantity of another good as '0'.

Vertical intercept = individual buys only Forst cola = I/P_FC

Vertical intercept = 800/10 = 80 Frost cola cases

Horizontal intercept = individual buys only Coca-cola = I/Pcc

Horizontal intercept = 800/20 = 40 Coca cola case

Ans b.) The eq(1) is the budget set equation which can further be written as :

800 = 10 × (FC) + 20 × (CC)

In the above figure , the black line depicts the budget constraint at given price and income.

It is downward sloping meaning that in order to purchase ine extra unit of coca cola , some units of frost cola must be give up. The slope of this budget constraint is as follows:

Slope = - P_cc/P_FC

Ans c.) If the price of Frost cola decreases to $5, the budget constraint tilt outwards from vertically as the consumer can now purchase more no. of Frost Colas at new price and income.

Ans d.) If the consumer purchases 7 cases of Coca-Cola, no. of Frost Cola that can be purchased with given income and new price can be calculated with the budget set as follows :

800 = 20 × (7) +  10 ×(FC )

800   = 140 +  10 × (FC)

660 = 10 × ( FC)

FC = 660 / 10

Frost Cola = 66 cases

Thus, the consumer can buy 66 cases of Frost cola if he buys 7 units of coca cola.