Which Of The Following Is Not A Source Of Decreasing Returns

Which Of The Following Is Not A Source Of Decreasing Returns To Sca

1. Which of the following is NOT a source of Decreasing Returns to Scale. A. Problem of coordination and control. B. Entrepreneurial capacity is fixed. C. Inflexibility. D. Cannot make fast decisions. E. Specialization in the use of capital and labor.

2. A firm has a demand function and a total cost function as follows: P=$5,000-$3Q TC=$300,000+$1,000Q+$2Q2. Calculate the optimal output and price under two scenarios: A. The firm is maximizing total profit. B. The firm is maximizing total revenue.

3. A firm has a demand function: Q=30-0.2P and a supply function: Q= -30+0.4P. Determine: A. the market equilibrium price (P) and quantity (Q). B. Using a graph, discuss how an increase in consumer income affects the market equilibrium price and quantity, assuming the product is a normal good.

4. The demand function for bicycles in Holland is estimated as: Q = 2,000 + 15Y – 0.5P, where Y is income in thousands of guilders, Q is the quantity demanded, and P is the price per unit. When P = 150 guilders and Y = 15 (thousand) guilders, determine: A. Price elasticity of demand. B. Income elasticity of demand.

Paper For Above instruction

Decreasing returns to scale (DRS) refer to a situation where, as a firm increases all input factors proportionally, the output increases by a lesser proportion. This concept is crucial in understanding productive efficiency and firm behavior in the long run. Identifying sources of DRS helps businesses and economists understand operational constraints and market dynamics. This paper discusses a common misconception regarding the sources of decreasing returns to scale, analyzes optimal production strategies based on demand and cost functions, examines market equilibrium conditions, and evaluates elasticity measures in response to price and income changes.

The question of what constitutes a source of decreasing returns to scale is fundamental in microeconomic theory. Often, firms experience DRS due to various internal and external factors. The provided options include issues like coordination problems, fixed entrepreneurial capacity, inflexibility, slow decision-making, and specialization in resource utilization. Notably, among these, the option "Specialization in the use of capital and labor" is typically associated with increasing returns to scale, as specialization tends to improve efficiency and productivity with increased scale (Samuelson & Nordhaus, 2010). Therefore, specialization is not a source of decreasing returns; instead, it usually leads to increasing returns or constant returns to scale, making it the correct choice for the question.

Understanding how firms determine their optimal output and price involves analyzing demand and cost functions. For the given demand function, P = $5,000 - $3Q, and total cost function, TC = $300,000 + $1,000Q + 2Q^2, the goal is to find the profit-maximizing and revenue-maximizing output levels. Profit maximization occurs where marginal revenue equals marginal cost, whereas revenue maximization occurs where marginal revenue is zero.

Deriving marginal revenue (MR) from the demand function involves expressing total revenue (TR) as TR = P × Q = ($5,000 - $3Q)Q = $5,000Q - $3Q^2. The MR is the derivative of TR with respect to Q: MR = d(TR)/dQ = $5,000 - 6Q. Setting MR equal to marginal cost (MC), which is the derivative of TC with respect to Q: MC = $1,000 + 4Q, allows solving for optimal Q under profit maximization:

$$ $5,000 - 6Q = $1,000 + 4Q \\ $$

This yields Q = 400 units. Substituting Q into the demand function gives the price: P = $5,000 - 3(400) = $5,000 - $1,200 = $3,800. Therefore, the profit-maximizing output is 400 units, with a price of $3,800.

In contrast, revenue maximization occurs when marginal revenue equals zero: $$0 = $5,000 - 6Q \\ Q = \frac{\$5,000}{6} \approx 833.33$$. The corresponding price is P = $5,000 - $3(833.33) ≈ $5,000 - $2,500 = $2,500.

Regarding market equilibrium, equate demand and supply: Q_D = Q_S. From demand: Q = 30 - 0.2P, and from supply: Q = -30 + 0.4P. Setting Q_D = Q_S gives:

$$ 30 - 0.2P = -30 + 0.4P \\ 60 = 0.6P \\ P = \$100$$.

Substituting P back into either function yields Q = 30 - 0.2(100) = 30 - 20 = 10 units. Thus, the equilibrium price is $100, and the equilibrium quantity is 10 units. A graphical representation would show shifts in demand or supply curves affecting these equilibrium points, especially considering the normative relation that higher income increases demand for normal goods, shifting the demand curve rightward and resulting in higher equilibrium prices and quantities.

Finally, elasticity measures the responsiveness of quantity demanded to price or income changes. The price elasticity of demand (PED) is calculated as:

$$ PED = \frac{\partial Q}{\partial P} \times \frac{P}{Q} $$

Given the demand function Q = 2000 + 15Y - 0.5P, at P = 150 and Y = 15,000 guilders, the quantity demanded is:

Q = 2000 + 15(15) - 0.5(150) = 2000 + 225 - 75 = 2150 units.

Derivative with respect to P: ∂Q/∂P = -0.5. Therefore, the price elasticity is:

$$ PED = -0.5 \times \frac{150}{2150} \approx -0.5 \times 0.0698 \approx -0.0349 $$

This indicates highly inelastic demand concerning price changes.

The income elasticity of demand (YED) is similarly computed as:

$$ YED = \frac{\partial Q}{\partial Y} \times \frac{Y}{Q} $$

∂Q/∂Y = 15, so:

$$ YED = 15 \times \frac{15,000}{2150} \approx 15 \times 6.977 \approx 104.65 $$

This high positive value signifies a strong demand response to income changes, characteristic of normal goods.

In conclusion, understanding the sources of decreasing returns to scale, optimizing output and price, analyzing market equilibrium, and calculating elasticity are fundamental concepts in microeconomics. Recognizing specialization as a factor that typically drives increasing returns, alongside a clear grasp of demand and cost functions, provides valuable insights for managerial decision-making and economic analysis.

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