Key Concepts in Economics: Impact on Supply, Demand, and Production

Posted on Dec 8, 2024 in Economy

1. How Does Product Quantity Demanded React to Increased Prices of Complements?

Explanation: Complementary products are goods that are often used together (e.g., printers and ink cartridges, or coffee machines and coffee pods). When the price of one complementary good increases, the overall cost of using the associated product bundle also increases.

Effect on Demand: An increase in the price of one complementary product reduces the demand for the other complementary product. For example, if the price of ink cartridges rises, consumers might buy fewer printers since using them becomes more costly. This relationship is reflected by a leftward shift in the demand curve of the associated product.

2. What Is the Effect of Decreased Personal Income Tax on Supply and Demand?

Explanation: A decrease in personal income tax increases consumers’ disposable income, allowing them to spend more on goods and services. This change affects the demand side of the market.

Effects on the Curves:

• Demand Curve: Increases in disposable income shift the demand curve to the right, as consumers are willing to buy more at each price level.
• Supply Curve: In the short run, supply remains unchanged if tax cuts only affect consumers and not producers.

Graphical Representation:

• The demand curve shifts to the right, indicating an increase in demand.
• The shift results in a higher equilibrium price and quantity.

3. Why Are Utility Curves Usually Convex?

Explanation: Convexity of Utility Curves: Utility curves, or indifference curves, are typically convex due to the principle of diminishing marginal rate of substitution (MRS). This means that as a consumer substitutes one good for another, they are willing to give up less of one good to get an additional unit of the other.

Intuition: Consumers prefer a balanced mix of goods rather than extremes. Convexity reflects this preference for diversity.

Exceptions: In cases of perfect substitutes, the utility curve is a straight line since consumers are willing to substitute one good for another at a constant rate. For perfect complements (like left and right shoes), utility curves are L-shaped because the goods must be consumed in fixed proportions to provide utility.

4. Should a Company Stop Producing When Marginal Production Decreases?

Answer: No, not necessarily. A decrease in marginal production (diminishing marginal returns) does not mean a company should stop producing. It only implies that adding additional units of an input (like labor) leads to smaller increases in output. A firm should continue producing as long as the marginal revenue from the additional output exceeds the marginal cost of the input. Production should stop when marginal cost equals marginal revenue, which is the profit-maximizing point.

Example: If hiring one more worker increases output but adds more to cost than revenue, then it’s time to stop adding more workers.

5. When to Use Short Run and Long Run in Economics?

Explanation: Short Run: A period during which at least one factor of production (like capital, land, or machinery) is fixed. Firms can adjust some inputs (like labor or raw materials) but cannot change their scale of operations significantly.

Example: A restaurant hiring extra staff for a busy weekend but not being able to expand the building.

Long Run: A period in which all factors of production are variable, allowing firms to adjust their scale of operations, enter or exit the market, or adopt new technologies.

Example: A firm building a new factory to expand its production capacity. The distinction lies in the flexibility firms have to change their input levels and adjust their production processes.

Supply and Demand Calculations

Given the following equation for supply and demand: Qs = 1300 + 300P; Qd = 4200 – 500P, calculate:

a. Clearance price

b. Clearance quantity

c. Elasticity price. (Suppose a change in the price of 1 unit)

d. Arc elasticity price. (Suppose a change in the price of 1 unit).

Let’s solve each part of the problem step-by-step:

Given:

• Supply equation: Qs = 1300 + 300P
• Demand equation: Qd = 4200 – 500P

a. Equilibrium (Clearance) Price

To find the equilibrium price, we set the quantity supplied equal to the quantity demanded:

Qs = Qd

1300 + 300P = 4200 – 500P

Let’s solve for P:

300P + 500P = 4200 – 1300

800P = 2900

P = 2900 / 800 = 3.625

Clearance Price:

P = 3.625 (i.e., $3.63)

b. Equilibrium (Clearance) Quantity

To find the equilibrium quantity, substitute the clearance price back into either the supply or demand equation.

Let’s use the supply equation:

Qs = 1300 + 300 * 3.625

Qs = 1300 + 1087.5 = 2387.5

Clearance Quantity:

Q = 2387.5 units

c. Price Elasticity of Demand

The price elasticity of demand measures how sensitive the quantity demanded is to a change in price. The formula for elasticity (Ed) is:

Ed = (dQ/dP) * (P/Q)

From the demand equation Qd = 4200 – 500P, we see that:

dQ/dP = -500

Using the equilibrium price P = 3.625 and the equilibrium quantity Q = 2387.5:

Ed = -500 * (3.625 / 2387.5)

Ed = -0.759

Interpretation: The price elasticity of demand is approximately -0.76, indicating that the demand is inelastic (i.e., not very responsive to changes in price).

d. Arc Elasticity of Demand

The arc elasticity formula is used when calculating elasticity over a range of prices. It is given by:

Earc = (ΔQ/ΔP) * ((P1 + P2)/(Q1 + Q2))

Let’s assume a change in price of ΔP = 1 unit. We’ll calculate the new quantity demanded for P = 4.625 and the original P = 3.625.

1. Calculate Qd at P = 4.625:

Qd = 4200 – 500 * 4.625 = 4200 – 2312.5 = 1887.5

2. Calculate the change in quantity:

ΔQ = 2387.5 – 1887.5 = 500

3. Calculate the arc elasticity:

Earc = (500 / 1) * ((3.625 + 4.625) / (2387.5 + 1887.5))

Earc = 500 * (8.25 / 4275)

Earc = 0.964

Arc Elasticity:

The arc elasticity of demand is approximately 0.96.

Production Analysis and Returns to Scale

Complete the table and answer the following questions.

a. At what levels of production does the company have increasing, decreasing, and constant returns on scale?

b. When should they stop adding production inputs?

WORKERS | OUTPUT | AVERAGE | MARGINAL

1 | 8 | |

2 | 18 | |

3 | 33 | |

4 | 44 | |

5 | 55 | |

6 | 62 | |

7 | 65 | |

8 | 64 | |

Step 1: Completing the Table

We’ll calculate:

• Average Product (AP):

  AP = Total Output / Number of Workers

• Marginal Product (MP):

  MP = Change in Output = Qn – Qn-1

Step 2: Analyzing Returns to Scale

Now, we’ll identify the ranges for increasing, constant, and decreasing returns to scale:

1. Increasing Returns to Scale: When Marginal Product (MP) is increasing.

   • From 1 to 3 workers, MP increases (8 → 10 → 15).

2. Constant Returns to Scale: When Marginal Product (MP) is constant.

   • From 3 to 5 workers, MP remains constant (11).

3. Decreasing Returns to Scale: When Marginal Product (MP) decreases.

   • From 5 to 8 workers, MP decreases (7 → 3 → -1).

Step 3: When Should the Company Stop Adding Inputs?

• The company should stop adding production inputs when the Marginal Product (MP) becomes zero or negative, as adding more inputs would decrease the total output and lead to inefficiencies.
• In this case, the MP turns negative at 8 workers (MP = -1). Thus, the company should stop at 7 workers where MP is still positive.

Summary Answers:

a. Levels of production with increasing, constant, and decreasing returns on scale:

• Increasing Returns: 1 to 3 workers
• Constant Returns: 3 to 5 workers
• Decreasing Returns: 5 to 8 workers

b. When should they stop adding production inputs?

• The company should stop adding inputs at 7 workers, as adding the 8th worker leads to a decrease in total output (negative MP).