Economics Problem Set 2

1. Sara will buy 6 cans of cola and 1 bag of popcorn. Sarah’s income is $12 a week,

which means she can afford either $12/$1.50=8 cola or $12/$3=4 bag of popcorn. Her budget line will go through Y-axis at 4 and X-axis at 4. The line will touch the indifference curve l1 at (6,1).[pic 1]

The marginal rate of substitution is the magnitude of the slope/gradient of Sara’s consumption point and it equals to the gradient/ slope of her budget line. Which is y = mx + c. So m is 4/8= 0.5.

Sara will buy 2 cans of cola and 2 bags of popcorn when the price of cola increases.  Sara’s new budget line will be tangent at (2,2) to the indifference curve l0.

Price of one Cola ($)

        Since price of cola increases [pic 2][pic 3][pic 4][pic 5][pic 6][pic 7][pic 8][pic 9]

1.                                                      to $3 while income remain
                                                                                     same, Sara will buy 6 cola [pic 10][pic 11][pic 12]

              3.0        at $1.50 and 2 at $3.0. The [pic 13]

        2.5        demand curve will go

                 2.0        through these two points.

                 1.5

                 1.0                                            D        

                 0.5

           0

                  1     2     3     4    5     6    7    8    Quantity of Cola per week

1. The substitution effect is 1 can of cola and the income effect is 3 cans of cola. We can reduce Sara’s income until her budget line move back to original indifference curve and tangent to it which is l1 in order to divide the price effect to substitution and income effect. The point it touches l1 is at 5 cans of cola. Thus, substitution effect is the decrease from 6 to 5 cans of cola along indifference curve l1. While the income effect is price effect-substitution effect. Since substitution effect is 1 and price effect is 4, the income effect will be 3.
2. Normal good because as income decreases, quantity consumed decreases.