Question

Suppose that you have a weekly budget of $60 to spend at Starbucks. At Starbucks you can either
buy coffee, which costs $6, or a scone, which costs $2.
(a) [10 pts] Draw your budget constraint showing the trade-off between coffee and scones. Assuming
that you spend equal amounts on both goods, draw an indifference curve showing the optimal
choice. Solve for the optimal bundle and label the optimum at point A. What is the marginal
rate of substitution at point A?

(b) [10 pts] Suppose the price of scones increases to $3.00. Graph the consequences of this change
in price. Assume that you now spend only 30% of your income on scones. Solve for and label
the new optimum as point B. What is the marginal rate of substitution at point B?

(c) [5 pts] Interpret the change in the marginal rate of substitution between points A and B.

Answer 1

Answer (a) :

(0,10) is point C.

Here in above working note optimal choice is at point A where an individual purchase 5 units of coffee and 15 units of scones of $ 6 and $2 each respectively.

5 units × $6 + 15 units × $2 = 30 + 30 = $60

$60 is weekly budget.

Above or below point A all combination will either sacrifice good x or good y. At point A maximum units are optimal choosen that is 15 units and 5 units.

MRS ( From point C to A ) = 0.33 ( Calculated in working note)

Answer (b) : Price of scones is increased to $3.

Less units of scones will be purchased that is 6 units.

More units of coffee will be purchased that is 7 units.

MRS at point B from point C = Loss of good y / gain of good x

= 10-7 / 0+6 = 3/6 = 0.5

Below is working note attached for reference.

Above budget constraint will be rotating leftward as good x price is rised to $3 which will force individual to purchase 20 units of Scones. And Good Y price is same so point is same as was before. Hence same units can be attainable by individual of Good Y.

Answer (c) MRS ( at point A ) is 0.33 and MRS (at point B ) is 0.5 which is increasing as point B is above A. It means more units of Y are purchased and Units of X is sacrificed.

*** MRS of point A and B is calculated from the point C. Gain and loss is calculated by considering point C that is 0 units of Good X and 10 unit of Good Y. (0,10)= Point C.

Kindly rate for my answer please ? and feel free to ask your doubts.