Question

Sophia spends all her money on gummy worms and apps for her smartphone. A pound of gummy worms and a smartphone app each cost $2 Sophia's parents giver an allowance of $80 and 2 pounds of gummy worms each month. Draw her opportunity set, assuming that she cannot sell the gummy worms to her friends. How does her opportunity set change if she can sell the gummy worms at the market price of $2?

Answer 1

Choice set or opportunity set is the set of options that the consumers can consume given the budget constraint and prices .

In the first part the budget constraint is $80.

In the first part, Since the 2 pound of gummy worms are not transferrable, it can't be used to sell in the market and increase the income of the consumer. This 2 pound of gumpy worm won't affect the budget constraint.

Budget constraint would be : 2G + 2S = 80( G- pounds of gumpy worm, S - Apps in smartphone)

or G + S = 40

or S = 40-G

Here G DOES NOT include the 2 gummy worm which he has , no matter what the price and budget constraint is ( since he can't sell it)

Therefore the actual number of pound of gummy worms she would be consuming = G + 2

the opportunity set is as shown in the Table

Gummy worms (pounds) Smartphone apps 80/= 40 2 2+1 2+3 = = 3 5 35 27 22 15 20 25 30 32 17 12 10 37 42

table 1

the diagram is

240) 4 (10,32) Smartphone (20,22) Obb32 I slope = -1 * ( 30, 12) 120 20 үИ ТИМ (О (0) Хма i pounds 42

fig 1

​​​​​​Part 2

in part 2, the budget constraint changes. Since Sophia can sell her endowment of 2 pound of gummy worms, her budget increases by $ (2*2) = $4

new budget constraint is = $ 84

here even if she is consuming one of her endowment say 1 gummy , she is forgoing the opportunity to sell it and instead buy smartphone app, i.e., she is forgoing 1 unit of smartphone ( prices are same)

2G + 2 S = 84

G + S = 42

G = 42 - S

Following table shows the choice set

Gummy worms (pounds) .. Smartphone app 42 yo 39 35 12 17 22 30 25 20 15 10 32 37 42

Table 2

The corresponding diagram is given below

42 12,30 Smartphone - (2121) app2 (3210) 32 Gummy worms (pounds)

Fig 2 : opportunity set when Sophia can sell her endowment