Scenario 1: Length As Needed For A Cupcake Store In A ✓ Solved

Scenario 1 Length As Needed A Cupcake Store Is Located In A Mall An

A cupcake store is located in a mall and is the only cupcake store in that mall. The demand schedule for cupcakes (per dozen) is given as follows: at $12, the quantity demanded is 3 dozen; at $11, it is 7; at $10, 12; at $9, 20; at $8, 35; at $7, 60; at $6, 100; and at $5, 160. The marginal cost to produce a dozen cupcakes is $4 per unit. Determine the optimal production quantity for the firm and the price it should charge. Additionally, if the fixed cost is $100 per day, calculate the daily profit. Evaluate the price elasticity of demand at the optimal price and quantity, using the next lower price level for elasticity calculation. Finally, verify whether the condition MR > MC aligns with the criterion (P - MC)/P > 1/elasticity as discussed in your course material.

Sample Paper For Above instruction

In a monopolistic market setting within a mall, a cupcake store faces a downward-sloping demand curve with an associated marginal cost of $4 per dozen. To determine the profit-maximizing output, the firm must analyze the demand schedule and compare marginal revenue with marginal cost, aiming to produce where MR = MC. The demand schedule provided indicates that as the price decreases, the quantity demanded increases significantly. Calculating marginal revenue at each relevant quantity helps identify the optimal output level.

At a price of $7 per dozen, the quantity demanded is 60 dozens. The total revenue (TR) at this point is $7 60 = $420. To find marginal revenue between $7 and $6, we note the change in TR: TR at $6 (100 dozens) is $6 100 = $600, and at $7 it was $420. The change in TR is $600 - $420 = $180, with the change in quantity being 100 - 60 = 40 dozens. Therefore, the approximate marginal revenue when decreasing the price from $7 to $6 is $180 / 40 = $4.50. Since MR ($4.50) is close to MC ($4), producing 60 dozens at a price of $7 seems optimal.

Charging $7 per dozen maximizes profit because at that point, MR approximately equals MC. The store should therefore set the price at $7. The profit can be calculated as follows: total revenue is $420, total cost is (fixed costs of $100 + variable costs of $4 * 60 = $240), totaling $340. Hence, daily profit is $420 - $340 = $80.

The price elasticity of demand at this point uses the two points at $7 and $6: Price change from $7 to $6, and corresponding quantity change from 60 to 100. The percentage change in quantity is (100 - 60)/60 = 0.6667, and the percentage change in price is ($6 - $7)/$7 = -0.1429. Elasticity = (0.6667) / (-0.1429) ≈ -4.67. The demand is elastic at this point, indicating a substantial response to price changes.

The condition MR > MC aligns with the profitability rule that profit maximization occurs where marginal revenue exceeds marginal cost. The formula (P - MC)/P > 1/elasticity must hold for continued profit maximization, which is satisfied in this case given the elastic nature of demand.

Sample Paper For Above instruction

In conclusion, the cupcake store should produce approximately 60 dozens of cupcakes daily, charging a price of $7 per dozen to maximize profits. The elasticity of demand at this point is highly elastic (around -4.67), asserting that minor changes in price can significantly impact quantity demanded. Ensuring MR equals or slightly exceeds MC is vital for profit maximization, and the condition (P - MC)/P > 1/elasticity) is satisfied in this scenario, confirming the economic rationality of the pricing and output decision. The analysis underscores the importance of understanding demand elasticity and marginal considerations in setting optimal prices in monopolistic markets or monopolistic-like settings such as single-store environments within a mall.

References

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