Let's answer each part step by step, explaining each step: --- ### (a) What are its short run variable costs and total fixed costs? #### **Step 1: Identify the short run cost function** The cost function is: \[ STC(q) = .5q^2 + 4q + .5 \] - **Fixed costs:** Terms that do **not** depend on \( q \) (output). - **Variable costs:** Terms that **do** depend on \( q \). #### **Step 2: Separate fixed and variable costs** - **Total Fixed Cost (TFC):** \( .5 \) (the constant term) - **Short Run Variable Cost (SVC):** \( .5q^2 + 4q \) (the terms with \( q \)) **Explanation:** - Fixed cost is what the firm has to pay even if output is zero (the constant). - Variable costs change with output (the terms that include \( q \)). --- **Final Answer (a):** - **Short run variable cost:** \( .5q^2 + 4q \) - **Total fixed cost:** \( .5 \) --- Would you like to continue with part (b) next?

Sure, let's solve all parts step by step. --- ### (a) What are its short run variable costs and total fixed costs? #### **Step 1: Identify the short run cost function** The cost function is: \[ STC(q) = 0.5q^2 + 4q + 0.5 \] - **Fixed costs:** Terms that do **not** depend on \( q \). - **Variable costs:** Terms that **do** depend on \( q \). #### **Step 2: Separate fixed and variable costs** - **Total Fixed Cost (TFC):** \( 0.5 \) (the constant term) - **Short Run Variable Cost (SVC):** \( 0.5q^2 + 4q \) (the terms with \( q \)) **Explanation:** - Fixed costs are expenses that remain constant regardless of output, while variable costs fluctuate with the level of production. --- **Final Answer (a):** - **Short run variable cost:** \( 0.5q^2 + 4q \) - **Total fixed cost:** \( 0.5 \) --- ### (b) What is the short run supply curve? #### **Step 1: Determine Marginal Cost (MC)** To find the supply curve, we first need to determine the marginal cost from the total cost function: \[ MC = \frac{d(STC)}{dq} = \frac{d(0.5q^2 + 4q + 0.5)}{dq} = q + 4 \] #### **Step 2: Identify the supply curve** In a perfectly competitive market, the supply curve is the portion of the MC curve that lies above the average variable cost (AVC). We need to calculate AVC: \[ AVC = \frac{SVC}{q} = \frac{0.5q^2 + 4q}{q} = 0.5q + 4 \] **Explanation:** The supply curve is determined by the marginal cost of production, as firms will only supply goods at prices above the average variable cost to cover their variable expenses. --- **Final Answer (b):** - **Short run supply curve:** \( MC = q + 4 \) (for prices above \( AVC \)) --- ### (c) What is the price of output in the short run? #### **Step 1: Equilibrium Price Determination** In a perfectly competitive market, the price is determined by the intersection of the market supply and demand curves. #### **Step 2: Use given market demand** Assuming the market demand is \( Q_d = 100 - P \) and supply is defined by the derived MC. Set \( Q_s = MC \) to find \( P \): \[ Q_s = 50 \quad (given \text{ number of firms}) \] **Explanation:** At equilibrium, the quantity supplied equals the quantity demanded, allowing us to find the market price when we know the supply and demand functions. --- **Final Answer (c):** - **Price of output:** Needs to be further calculated based on the intersection of demand and supply equations. --- ### (d) What is the cost of output? #### **Step 1: Calculate Total Cost at equilibrium quantity** Using \( q \) from the supply curve, the total cost can be calculated: \[ TC = STC(q) = 0.5q^2 + 4q + 0.5 \] #### **Step 2: Substitute equilibrium quantity** Once we determine the equilibrium quantity \( q \), substitute it into the total cost function. **Explanation:** The total cost reflects the full economic cost of producing the output at the equilibrium quantity. --- **Final Answer (d):** - **Cost of output:** Needs to be calculated based on equilibrium quantity. --- ### (e) What is the economic profit? #### **Step 1: Calculate Profit** Profit is given by: \[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} \] #### **Step 2: Determine Total Revenue** Total revenue is calculated as: \[ TR = P \times q \] **Explanation:** Economic profit indicates the difference between total revenues and total costs, providing insight into the firm's financial performance. --- **Final Answer (e):** - **Economic profit:** Requires equilibrium price and quantity for calculation. --- ### (f) What is the cumulative value of output in the market over 30 months? #### **Step 1: Calculate monthly output** If each firm produces quantity \( q \) and there are \( 50 \) firms, total market output is: \[ Q = 50 \times q \] #### **Step 2: Calculate total output over 30 months** Total output over 30 months is: \[ \text{Total Output} = Q \times 30 \] **Explanation:** This gives the total market output over the specified time period, reflecting the cumulative production of the firms. --- **Final Answer (f):** - **Cumulative value of output over 30 months:** Requires equilibrium quantity for calculation. --- ### (g) What is the market equilibrium economic profit? #### **Step 1: Identify long-term equilibrium** In long-run equilibrium, economic profit becomes zero as firms enter or exit the market. #### **Step 2: Analyze potential scenarios** If firms can earn economic profit in the short run, new firms will enter until profits are zero. **Explanation:** In perfect competition, long-run equilibrium is characterized by zero economic profit as market forces balance supply and demand. --- **Final Answer (g):** - **Market equilibrium economic profit:** Zero in the long run. --- If you need further elaboration on any part or specific calculations, feel free to ask!