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1.You have an income of 50 to spend on two commodities, ice cream and cookies. I...

Sep 14, 2024

1.You have an income of 50 to spend on two commodities, ice cream and cookies. Ice cream costs

5 per scoop, and cookies cost

2.50 each. (a)Write down your budget equation. (b)If you spent all your income on ice cream, how much could you buy? (c)If you spent all of your income on cookies, how much could you buy? (d)Draw a diagram of this budget line. (e)What is the rate of exchange of ice cream for cookies? (f)Suppose the price of cookies decreases to

2.00 and ice cream prices are not changed. Draw the new budget line (on the same diagram as part d). (g)What happened to the rate of exchange between ice cream and cookies? (h)Now suppose your income increases to

100. Draw your new budget line. (i)At your income of

100, with cookie prices of

2.00, suppose that ice cream prices rise to $20 per scoop. After drawing the new budget line, compare the outcomes of (d) and (i). What can you say? Note: there are lots of budget lines and diagrams. Please make sure I can follow your work, so you might need to make many diagrams. Use your judgment! 2.I have a small slush fund devoted to candy and books. I can purchase 8 candy bars and 8 books a month. Alternatively, I can buy 10 candy bars and 4 books a month. The price of a candy bar is 50 cents. Draw my budget line and write the budget equation. How much money is in my monthly slush fund? 3.You spend your income on “food” and “car services.” In the first situation, car services come in the form of owning: no cars, in which your car services are 0 or no services; one car, in which you have low services; or 2 cars which gives you high services. You cannot afford 3 cars, even if you forgo all food. What does your budget constraint (car services on one axis, food on the other) look like? a.Now supposed you can hire car services (such as paying for uber rides). What does your budget constraint look like, if you can only hire car services and cannot own a car outright? 4.Problem 2 in “To think about section” of Kreps, page 58. To think about this question use a budget constraint to model Food and All other products. Vary the assumptions and draw some budget lines to think about food comprising 10 percent, 25 percent, 50 percent and 80 percent of income. Consider how family size might change the situation.

Solution by Steps

Question 1:

step 1

The budget equation can be written as:

5x + 2.5y = 50

, where

x

is the number of ice cream scoops and

y

is the number of cookies

step 2

If all income is spent on ice cream, the number of scoops is:

\frac{50}{5} = 10

step 3

If all income is spent on cookies, the number of cookies is:

\frac{50}{2.5} = 20

step 4

The budget line can be drawn with ice cream on the x-axis and cookies on the y-axis, connecting the points (10, 0) and (0, 20)

step 5

The rate of exchange of ice cream for cookies is the ratio of their prices:

\frac{5}{2.5} = 2

step 6

If the price of cookies decreases to $2.00, the new budget equation is: $ 5x + 2y = 50 $. The new intercepts are (10, 0) and (0, 25)

step 7

The new rate of exchange is

\frac{5}{2} = 2.5

, indicating that ice cream is now more expensive relative to cookies

step 8

With an income of $100, the budget equation becomes: $ 5x + 2.5y = 100 $. The intercepts are (20, 0) and (0, 40)

step 9

If ice cream prices rise to $20 per scoop, the new budget equation is: $ 20x + 2y = 100 $. The intercepts are (5, 0) and (0, 50)

step 10

Comparing the budget lines from (d) and (i), the new budget line shows a significant decrease in the quantity of ice cream that can be purchased, indicating a reduced purchasing power for ice cream

1 Answer

--- Question 2:

step 1

The budget equation can be written as:

0.5c + b = M

, where

c

is the number of candy bars,

b

is the number of books, and

M

is the total money in the slush fund

step 2

From the first scenario,

0.5(8) + 8 = M

gives

M = 12

step 3

From the second scenario,

0.5(10) + 4 = M

gives

M = 9

step 4

The slush fund must be at least $12 to afford the maximum combination of candy bars and books

2 Answer

--- Question 3:

step 1

The budget constraint can be represented as:

c + f = M

, where

c

is the number of cars and

f

is the amount spent on food

step 2

The maximum number of cars is 2, so the budget constraint can be plotted with points (0, M) and (2, 0)

step 3

If only hiring car services, the budget constraint becomes:

s + f = M

, where

s

is the amount spent on services

step 4

The new budget line will have a different slope, reflecting the cost of hiring services instead of owning cars

3 Answer

--- Question 4:

step 1

The budget constraint for food and all other products can be modeled as:

f + o = I

, where

f

is food,

o

is other products, and

I

is income

step 2

For different percentages of income spent on food, the budget lines will shift accordingly. For example, if food is 10% of income, the equation becomes

0.1I + o = I

step 3

As family size increases, the budget line may shift outward, allowing for more food and other products to be purchased

4 Answer

---

Key Concept

Budget Constraints

Explanation

Budget constraints illustrate the trade-offs between different goods based on income and prices, showing how changes in prices or income affect purchasing decisions.