Complete the following table. Graph total revenue, average revenue and marginal revenue curves. Explain the relation of total revenue and marginal revenue with price elasticity of demand. (2+3+5)…

Solution to the Problem

1. Completing the Table

We are given the Total Revenue (TR) for different quantities. We need to calculate Average Revenue (AR) and Marginal Revenue (MR).

• Average Revenue (AR) is calculated as: $$AR=\frac{TR}{Q}$$
• Marginal Revenue (MR) is the change in Total Revenue when one additional unit is sold: $$MR=T{R}_n-T{R}_{n-1}$$

Let’s compute the values step-by-step:

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2. Graphing Total Revenue (TR), Average Revenue (AR), and Marginal Revenue (MR)

We plot the following curves based on the computed values:

Observations from the Graph:

• TR increases up to Q = 30, reaches a maximum, and then declines.
• AR is a straight line (since demand is linear in this case) and slopes downward.
• MR is a straight line below AR, intersecting at Q = 30 (where MR = 0).

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3. Relationship Between Total Revenue, Marginal Revenue, and Price Elasticity of Demand

The relationship between TR, MR, and Price Elasticity of Demand (PED) can be explained as follows:

(a) When MR > 0 (Elastic Demand)

• If MR is positive, selling an additional unit increases TR.
• This happens when PED > 1 (elastic demand).
• In the table, for Q = 0 to 30, MR is positive, and TR is increasing.
• Example: At Q = 20, MR = 40, meaning each additional unit increases TR by 40.

(b) When MR = 0 (Unit Elastic Demand)

• If MR = 0, TR is at its maximum.
• This occurs when PED = 1 (unit elastic demand).
• In the table, at Q = 30, MR = 0, and TR is at its peak (120).

(c) When MR < 0 (Inelastic Demand)

• If MR is negative, selling an additional unit decreases TR.
• This happens when PED < 1 (inelastic demand).
• In the table, for Q = 40 to 70, MR is negative, and TR declines.
• Example: At Q = 50, MR = -20, meaning each additional unit reduces TR by 20.

Mathematical Relationship:

The Price Elasticity of Demand (PED) can be derived from MR and AR as: $$PED=\frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}=\frac{MR}{AR}\times \frac{Q}{P}$$ But since AR = Price (P), we can simplify: $$PED=\frac{MR}{P}\times \frac{Q}{P}=\frac{MR\cdot Q}{P^2}$$ However, a simpler rule is:

• If MR > 0, demand is elastic (PED > 1).
• If MR = 0, demand is unit elastic (PED = 1).
• If MR < 0, demand is inelastic (PED < 1).

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4. Explanation with Real-World Implications

• Firms maximize profit where MR = MC (Marginal Cost).
  • If MR > MC, the firm should increase production (since each additional unit adds more to revenue than cost).
  • If MR < MC, the firm should decrease production (since each additional unit reduces profit).
• TR and MR help in pricing decisions:
  • If a firm is in an elastic demand region (MR > 0), a price cut increases TR.
  • If a firm is in an inelastic demand region (MR < 0), a price cut decreases TR.
• Example:
  • A luxury car manufacturer (elastic demand) may lower prices to increase sales and TR.
  • A necessity like salt (inelastic demand) may increase prices without losing many customers.

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5. Summary of Key Relationships