Title: Economics Problem Set
Abstract:
- Content: Series of microeconomics problems.
- Topics: Utility maximization, budget constraints, production costs, marginal analysis, opportunity cost.
- Tasks:
- Calculate marginal utility, marginal cost, marginal product of labor.
- Graph total utility curves, budget constraints, total cost curves.
- Analyze slopes and economic interpretations.
- Decision-making based on marginal analysis.
Module 3 Assignment
An Economic Framework for Decision-Making
(50 points)
Name: ________________________________
1. The table below shows the total utility (satisfaction), measured in dollars, that Álvaro receives from eating seven slices of pepperoni pizza.
a) Calculate the marginal utility provided by each slice that Álvaro eats. Show your work (3 points).
|
Slices of Pizza Consumed |
Total |
Marginal (MU) |
|
1 |
$20 |
N/A |
|
2 |
$35 |
|
|
3 |
$45 |
|
|
4 |
$52 |
|
|
5 |
$58 |
|
|
6 |
$59 |
|
|
7 |
$45 |
|
b) Explain why economists use monetary units (dollars) to measure utility (1 point).
c) If the cost of each pizza slice is $6, how many slices will Álvaro eat to maximize his utility? Explain your answer (2 points).
d) If each pizza slice is free, how many slices will Álvaro eat to maximize his utility? Explain your answer (2 points).
e) Graph Álvaro’s total utility curve. Do not forget to label the axes (2 points).
Total Utility Curve
f) What does the slope of the total utility curve represent? (1 point)
g) How does the slope help explain the shape of the total utility curve? (1 point).
2. Assume that Álvaro has a disposable income of $120 per month and that he likes to spend all that disposable income on just two goods: Wine and cheese.
a) If the cost of a glass of wine is $3, how many glasses can Álvaro afford to drink if he chooses to spend all his disposable income on wine? Show your work (2 points).
b) If the cost of a pound of cheese is $6, how many pounds can Álvaro afford to eat if he chooses to spend all his disposable income on cheese? Show your work (2 points).
c) Draw Álvaro’s budget constraint with wine on the y-axis. Graph three points on the line, including the corner solutions from 1.a. and 1.b. Do not forget to label the axes (3 points).
d) Calculate the slope of Álvaro’s budget constraint. Show your work (2 points).
e) What does the slope represent in terms of Álvaro’s ability to buy wine and cheese? (1 point).
3. The graph below represents two budget constraints for the same individual.
a) What is represented by a single point on a budget constraint? (1 point)
b) What is represented by the entire line of a budget constraint? (1 point)
c) What specific change would make the individual switch from the blue budget constraint to the pink budget constraint? Explain your answer (1 point).
d) If the income of the consumer is $10, what is the price of one bus ticket according to the blue budget constraint? Show your work (1 point).
e) If the income of the consumer is $10, what is the price of one burger according to the blue budget constraint? Show your work (1 point).
f) If the income of the consumer is $10, what is the price of one bus ticket according to the pink budget constraint? Show your work (1 point).
g) If the income of the consumer is $10, what is the price of one burger according to the pink budget constraint? Show your work (1 point).
h) What is the opportunity cost of buying an additional bus ticket according to the blue budget constraint? Show your work (1 point).
i) What is the opportunity cost of buying an additional burger according to the blue budget constraint? Show your work (1 point).
j) What is the opportunity cost of buying an additional bus ticket according to the pink budget constraint? Show your work (1 point).
k) What is the opportunity cost of buying an additional burger according to the pink budget constraint? Show your work (1 point).
4. The information below represents the daily production costs at Álvaro’s coffee shop, which specializes in caramel macchiatos.
a) Calculate the marginal cost of producing each caramel macchiato. Show your work (3 points).
|
Quantity of Caramel Macchiatos |
Total Cost (TC) |
Marginal Cost (MC) |
|
0 |
$30 |
N/A |
|
1 |
$32 |
|
|
2 |
$35 |
|
|
3 |
$40 |
|
|
4 |
$46 |
|
|
5 |
$53 |
|
|
6 |
$62 |
|
b) If each caramel macchiato is sold at a price of $6, how many caramel macchiatos will Álvaro produce to maximize his profit? Explain your answer (2 points).
c) Graph the total cost curve for Álvaro’s coffee shop. Do not forget to label the axes (2 points).
Total Cost Curve
d) What does the slope of the total cost curve represent? (1 point).
e) How does the slope help explain the shape of the total cost curve? (1 point)
5. Imagine that you spent Labor Day weekend fishing. After a few hours, you notice the following relationship between the time spent fishing and the quantity of fish caught:
a) Calculate the marginal product of each hour you spent fishing. Show your work (3 points).
|
Hours (Input) |
Quantity |
Marginal Product of |
|
0 |
0 |
N/A |
|
1 |
10 |
|
|
2 |
18 |
|
|
3 |
24 |
|
|
4 |
28 |
|
|
5 |
30 |
|
b) What are the two general reasons why most production processes exhibit diminishing marginal product of labor? (2 points)
1.
2.
c) Why is the marginal product of labor diminishing in this specific scenario? (1 point)
d) Imagine that the opportunity cost of your time is $30 per hour (that is what you would earn working at your job) and that you can sell each fish you catch for a price of $6. Using marginal analysis, determine how many hours you should spend fishing (versus working) to maximize your earnings. Show your work (2 points).