### Long-Run Total Cost Function and Market Analysis**Problem Statement:**Suppose that the identical firms in a perfectly competitive market for cakes have long-run total cost functions given by:\[ TC(Q) = 10Q^3 - 60Q^2 + 100Q. \]Total cost is independent of the number of firms and total output in the market. If market demand is $Q^D = 1,000 - 40P$, solve for the following:1. Output per firm (Q)2. Long-run competitive equilibrium price (P)3. Market demand ($Q^D$)4. Number of firms in the market (N)**Explanation:**1. **Total Cost Function (TC(Q)):** The cost incurred by each firm in producing quantity $Q$ is given by: \[ TC(Q) = 10Q^3 - 60Q^2 + 100Q. \]2. **Market Demand Curve:** The market demand for cakes is represented by the demand equation: \[ Q^D = 1,000 - 40P. \]**To Solve:**1. **Output per firm (Q):** In a perfectly competitive market, firms will increase their production until the marginal cost (MC) equals the market price (P). The marginal cost (MC) can be derived from the total cost (TC) function.2. **Long-run competitive equilibrium price (P):** At long-run equilibrium, the price (P) is equal to the minimum average total cost (ATC).3. **Market Demand ($Q^D$):** Using the market demand equation, substitute the price (P) found in step 2 to find the total market demand.4. **Number of firms in the market (N):** The number of firms can be found by dividing the total market demand ($Q^D$) by the output per firm (Q).**Detailed Steps:**- **Calculate Marginal Cost (MC):** \[ MC = \frac{d(TC)}{dQ} = 30Q^2 - 120Q + 100. \] - **Calculate Average Total Cost (ATC):** \[ ATC = \frac{TC(Q)}{Q} = \frac{10Q^3 - 60Q^

To calculate P we know that MC is equal to The ATC in the long-run supply curve because the…

Suppose that the identical firms in a perfectly competitive market for cakes have long-run total cost functions given by TC(Q) = 1003 – 60Q² + 100Q. Total cost is independent of the number of firms and total output in the market. If market demand is QD = 1,000 – 40P, solve for the output per firm (Q), the long-run competitive equilibrium price (P), the market demand (Qº), and number of firms in the market (N).

Suppose that the identical firms in a perfectly competitive market for cakes have long-run total cost functions given by TC(Q) = 1003 – 60Q² + 100Q. Total cost is independent of the number of firms and total output in the market. If market demand is QD = 1,000 – 40P, solve for the output per firm (Q), the long-run competitive equilibrium price (P), the market demand (Qº), and number of firms in the market (N).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter12: The Partial Equilibrium Competitive Model

Section: Chapter Questions

Problem 12.9P

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