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Answer :
Below is a step-by-step explanation showing how each part of the problem is solved.
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Step 2: Earning Enough for a Comic Book
A comic book costs
[tex]$$20,$$[/tex]
and the wage is
[tex]$$20 \text{ dollars per hour}.$$[/tex]
The time needed to earn enough is calculated by dividing the cost by the hourly wage:
[tex]$$\text{Time} = \frac{20}{20} = 1 \text{ hour}.$$[/tex]
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Step 3: After a 5% Wage Increase and 10% Inflation on Comics
After a 5% increase, the new hourly wage becomes:
[tex]$$20 \times 1.05 = 21 \text{ dollars per hour}.$$[/tex]
With 10% inflation, the new cost of a comic book becomes:
[tex]$$20 \times 1.10 = 22 \text{ dollars}.$$[/tex]
In one hour at the new wage, the number of comic books you can afford is:
[tex]$$\frac{21}{22} \approx 0.9545 \text{ comic books}.$$[/tex]
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Step 4: Number of [tex]$10 Pizzas with a Monthly Salary of $[/tex]100
Each pizza costs
[tex]$$10 \text{ dollars},$$[/tex]
and the monthly salary is
[tex]$$100 \text{ dollars}.$$[/tex]
The number of pizzas you can buy initially is:
[tex]$$\frac{100}{10} = 10 \text{ pizzas}.$$[/tex]
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Step 5: After a 2% Salary Increase and 10% Inflation on Pizzas
After a 2% salary increase, the new monthly salary becomes:
[tex]$$100 \times 1.02 = 102 \text{ dollars}.$$[/tex]
With 10% inflation, the new cost of a pizza becomes:
[tex]$$10 \times 1.10 = 11 \text{ dollars}.$$[/tex]
The number of pizzas you can now buy monthly is:
[tex]$$\frac{102}{11} \approx 9.2727 \text{ pizzas}.$$[/tex]
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Step 6: Determining the Change in Real Wages
Real wages are measured by the purchasing power—in this case, the number of pizzas you can buy.
Initially, you could buy 10 pizzas per month. With the changes, you can buy about 9.27 pizzas.
Since
[tex]$$9.27 < 10,$$[/tex]
the real wage, or purchasing power, has decreased.
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Summary of Results:
1. It takes [tex]$1$[/tex] hour to earn enough for one comic book initially.
2. After the changes, in one hour, you can afford approximately [tex]$\frac{21}{22} \approx 0.9545$[/tex] comic books.
3. Initially, you can buy [tex]$10$[/tex] pizzas with your monthly salary.
4. After the changes, you can buy approximately [tex]$9.2727$[/tex] pizzas.
5. The real wage, in terms of pizza purchasing power, has decreased.
This completes the detailed solution.
–––––––––––––––––––––––––––––––––––––––
Step 2: Earning Enough for a Comic Book
A comic book costs
[tex]$$20,$$[/tex]
and the wage is
[tex]$$20 \text{ dollars per hour}.$$[/tex]
The time needed to earn enough is calculated by dividing the cost by the hourly wage:
[tex]$$\text{Time} = \frac{20}{20} = 1 \text{ hour}.$$[/tex]
–––––––––––––––––––––––––––––––––––––––
Step 3: After a 5% Wage Increase and 10% Inflation on Comics
After a 5% increase, the new hourly wage becomes:
[tex]$$20 \times 1.05 = 21 \text{ dollars per hour}.$$[/tex]
With 10% inflation, the new cost of a comic book becomes:
[tex]$$20 \times 1.10 = 22 \text{ dollars}.$$[/tex]
In one hour at the new wage, the number of comic books you can afford is:
[tex]$$\frac{21}{22} \approx 0.9545 \text{ comic books}.$$[/tex]
–––––––––––––––––––––––––––––––––––––––
Step 4: Number of [tex]$10 Pizzas with a Monthly Salary of $[/tex]100
Each pizza costs
[tex]$$10 \text{ dollars},$$[/tex]
and the monthly salary is
[tex]$$100 \text{ dollars}.$$[/tex]
The number of pizzas you can buy initially is:
[tex]$$\frac{100}{10} = 10 \text{ pizzas}.$$[/tex]
–––––––––––––––––––––––––––––––––––––––
Step 5: After a 2% Salary Increase and 10% Inflation on Pizzas
After a 2% salary increase, the new monthly salary becomes:
[tex]$$100 \times 1.02 = 102 \text{ dollars}.$$[/tex]
With 10% inflation, the new cost of a pizza becomes:
[tex]$$10 \times 1.10 = 11 \text{ dollars}.$$[/tex]
The number of pizzas you can now buy monthly is:
[tex]$$\frac{102}{11} \approx 9.2727 \text{ pizzas}.$$[/tex]
–––––––––––––––––––––––––––––––––––––––
Step 6: Determining the Change in Real Wages
Real wages are measured by the purchasing power—in this case, the number of pizzas you can buy.
Initially, you could buy 10 pizzas per month. With the changes, you can buy about 9.27 pizzas.
Since
[tex]$$9.27 < 10,$$[/tex]
the real wage, or purchasing power, has decreased.
–––––––––––––––––––––––––––––––––––––––
Summary of Results:
1. It takes [tex]$1$[/tex] hour to earn enough for one comic book initially.
2. After the changes, in one hour, you can afford approximately [tex]$\frac{21}{22} \approx 0.9545$[/tex] comic books.
3. Initially, you can buy [tex]$10$[/tex] pizzas with your monthly salary.
4. After the changes, you can buy approximately [tex]$9.2727$[/tex] pizzas.
5. The real wage, in terms of pizza purchasing power, has decreased.
This completes the detailed solution.
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