Scenario 1 Length As Needed A Cupcakestore Is Located In A M

Scenario 1 Length As Neededa Cupcakestoreis Located In A Mall And I

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 in the table below. If the marginal cost to produce a dozen cupcakes is $4 per unit, how many units should the firm produce? What price should the cupcake store charge? If the fixed cost for the firm is $100 per day, how much profit will the firm make in one day? What is the price elasticity of demand at the optimal price/quantity combination (use the next lower price level as the second point in your calculation)? Is the formula for finding the correct level of output on the bottom of page 65 in your text satisfied? MR > MC means that (P-MC)/P > 1/lel

Paper For Above instruction

The scenario presented involves determining the optimal production and pricing strategy for a cupcake store located in a mall, given its demand schedule, marginal costs, fixed costs, and the concept of price elasticity of demand. The analysis integrates concepts from microeconomic theory, including profit maximization, marginal analysis, and elasticity calculations.

To identify the optimal output quantity, the firm must compare marginal revenue (MR) with marginal cost (MC). Since the demand schedule is provided, the first step involves calculating the marginal revenue at various quantities to determine where MR equals MC. Given that the marginal cost is $4 per dozen, the store should produce the quantity where MR just exceeds or equals $4. Typically, in monopolistic or single-price scenarios, MR is derived from the demand curve by doubling the slope or by calculating total revenue changes. Assuming the demand schedule is linear, the MR corresponding to each price and quantity can be calculated from total revenue (TR = Price × Quantity), with MR being the derivative of TR with respect to quantity. The optimal output is achieved at the quantity where MR = MC = $4.

Once the optimal quantity is established, the store should set the price based on the demand schedule at that quantity. Since the demand schedule indicates the price consumers are willing to pay for different quantities, the price corresponding to the chosen quantity will maximize profit. The degree of price elasticity of demand at this point can be calculated by taking the percentage change in quantity demanded over the percentage change in price, specifically using the next lower price point for comparison.

The price elasticity of demand at the optimal point is given by the formula:

\( \varepsilon = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} \)

Using the two points from the demand schedule, the elasticity can be calculated to determine whether demand is elastic, inelastic, or unit elastic, which influences the firm's pricing decisions.

Finally, the analysis considers the profit calculation. The daily profit is obtained by subtracting total costs from total revenue. Total costs include fixed costs ($100 per day) plus variable costs, which are the marginal costs multiplied by the quantity produced. The profit formula is:

\( \text{Profit} = \text{Total Revenue} - \text{Total Costs} \)

where:

  • Total Revenue = Price at optimal quantity × optimal quantity
  • Total Costs = Fixed costs + (Marginal cost × optimal quantity)

In conclusion, the store should produce the quantity where MR=MC and set the price according to the demand at that quantity. Calculating the elasticity informs pricing strategies and helps ensure the firm maximizes its profit while respecting consumer responsiveness.

References

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