Question

3 Budget Constraints (5 points) Freddy the Meek has S24 to spend on waffles W and French Toast F. The prices are $2.5 and $7, respectively (a) What is the budget constraint? (1) (b) How many more waffles does an additional dollar spent on W buy? How many more French Toasts does an additional dollar spent on F buy? (1) (c) Can Freddy afford the bundle (2,3)? Can he afford the bundle (4,2)? (1) d) How many waffles does Freddy have to give up if he wants to buy two French Toasts more and keep spending constant? (1) (e) Currently Freddy plans to consume 4 waffles and 2 French Toasts. Then the prices rise by 20% for waffles and %30 for French Toast. How much additional income does Freddy need to consume the same amounts as before? (1)

Answer 1

a) Let the quantities of waffles and french toasts be denoted by x and y respectively.

Given prices of waffles and french toasts are $2.5 and $7 respectively. Also, budget is given $24.

Hence , the equation of the budget constraint is P_xx + P_yy = budget (where P_x and P_y are prices of x and y respectively).

or, 2.5x + 7y = 24 is the budget line.

b) As the price of both waffles and french toast are above 1$ so an additional dollar won't buy any more item.

c) For the bundle (2,3) , budget = 2.5*2+3*7 = $26 which is greater than Freddy's maximum budget of $24. Thus, Freddy cannot afford this bundle.

For the bundle (4,2) , budget = 2.5*4+2*7 = $24 which is equal to maximum budget of Freddy . Hence, he can afford this bundle.

d) Price of two french toast = 2*$7 = $14 .

Hence to buy two more french toast Freddy has to give up $14/$2.5 waffles = 5.6 $\approx$ 5 waffles.

e) Now, Freddy plans to consume 4 waffles and 2 french toasts .

At initial prices budget = 4*2.5 + 2*7 =$24

When, rise in prices of waffles is 20% , new price = $2.5 + 20/100*2.5 = 120*2.5/100 = $3

When, rise in price of french toast is 30% , new price = $7 +30/100*7 = 130*7/100 = $9.1

Hence , new budget with same consumption = 4*3 + 2*9.1 = $30.2

Hence, additional income required = $(30.2-24) = $6.2 i.e., 6.2/24*100 = 25.83% rise in income.