Instructor Ram Sewak Dubey Econ 317 Problem Set 8 December 3

Instructor Ram Sewak Dubey Econ 317 Problem Set 8 December 3 20181

Analyze various elasticity measures, production functions, and public policy concepts as outlined in the problem set instructions. This includes calculating price, income, and cross-price elasticities, as well as determining homogeneity and returns to scale of given production functions. Additionally, examine the structure and influence of the U.S. federal bureaucracy and compare types of public policies.

Paper For Above instruction

The study of elasticity measures—price elasticity of demand, income elasticity, and cross-price elasticity—is fundamental in understanding consumer behavior and market dynamics. Economists utilize these measures to assess how quantity demanded responds to changes in price or income, informing effective policy and business strategies. This paper examines the calculation of these elasticities based on provided demand functions, explores the concepts of homogeneity and returns to scale in production functions, and assesses the structure and influence of the U.S. federal bureaucracy as well as various public policy types.

Elasticity Analysis

The first segment involves calculating the price elasticity of demand and income elasticity using the given demand function Q=700−2P+0.02Y, where P=25 and Y=5000. Price elasticity of demand (ε) measures the responsiveness of quantity demanded to a change in price and is calculated as ε = (∂Q/∂P) (P/Q). Given the demand function, the derivative with respect to P is -2, indicating a constant slope. Substituting P=25 and Y=5000, the quantity demanded (Q) can be calculated as 700−2(25)+0.02(5000)=700−50+100=750. The price elasticity of demand becomes: ε = -2 (25/750) ≈ -0.0667, indicating inelastic demand at this point.

Similarly, the income elasticity (η) is computed as η = (∂Q/∂Y) (Y/Q). The derivative of Q with respect to Y is 0.02. Substituting the values, η = 0.02 (5000/750) ≈ 0.1333, indicating a normal good with a relatively inelastic response to income changes.

The second section examines the cross-price elasticity of demand for good 1, based on the demand function Q1=100−P1+0.75P2−0.25P3+0.0075Y, with specified values. Cross-price elasticity (ε12) is computed as (∂Q1/∂P2) (P2/Q1). The partial derivative of Q1 with respect to P2 is 0.75. Substituting the values, ε12 = 0.75 (20/170) ≈ 0.088. This positive value indicates substitutability between goods 1 and 2. Similarly, ε13 = (∂Q1/∂P3) (P3/Q1) with ∂Q1/∂P3 = -0.25 yields ε13 = -0.25 (40/170) ≈ -0.059, suggesting goods 1 and 3 are complements.

The third segment involves a more complex demand function Q1=50−4P1−3P2+2P3+0.001Y, with given values. The cross-price elasticities are computed similarly: for good 2, ε12 = (−3)(7/26) ≈ -0.81, indicating complements; for good 3, ε13 = 2(3/26) ≈ 0.23, indicating substitutes. Income elasticity is η = 0.001 * (11000/26) ≈ 0.423, suggesting normal demand. The effects of a 10% price increase in each good are calculated by multiplying the percentage change by the elasticity, resulting in estimated changes in quantity demanded. For example, a 10% increase in P2 leads to a decrease in Q1 by approximately 8.1 units, demonstrating sensitivity of demand to price shifts.

Homogeneity and Returns to Scale in Production

Homogeneity of a production function relates to whether the function exhibits constant, increasing, or decreasing returns to scale, characterized by the degree of homogeneity. If a function is homogeneous of degree k, scaling all inputs by a factor λ results in output scaling by λ^k. For each production function, the degree of homogeneity is determined by scaling inputs and observing the resulting change in output.

(a) Q= x^2 + 6xy + 7y^2 is homogeneous of degree 2 because each term consists of variables raised to the second degree, and scaling x and y by λ results in output scaling by λ^2, indicating constant returns to scale of degree 2.

(b) Q= x^3− xy^2 + 3y^3 + x^2 y is homogeneous of degree 3, as evidenced by each term being cubic in x and y, hence exhibiting constant returns to scale of degree 3.

(c) Q= 3x^2 5y^2 simplifies to a homogeneous function of degree 4, indicating increasing returns to scale if inputs are scaled.

Other functions such as Q= 0.5K^0.2L^0.6 are homogeneous of degree 0.8, showing decreasing returns to scale. The analysis involves scaling inputs and examining how output responds, confirming the nature of returns to scale.

Structure and Influence of the U.S. Federal Bureaucracy

The U.S. federal bureaucracy comprises various elements, including civil servants, government corporations, cabinet departments, independent regulatory agencies, and independent executive agencies. Civil servants, appointed and career officials, implement policies and administer programs, influencing political processes through policy execution. Government corporations operate as business entities, providing public services that generate revenue, such as the U.S. Postal Service, affecting market operations and public policy implementation (Moe, 2018).

Cabinet departments, led by secretaries, coordinate policy across sectors, shaping national priorities and the legislative agenda. Independent regulatory agencies oversee specific industries, ensuring compliance and protecting public interests, often affecting economic regulation (Kettl, 2017). Independent executive agencies perform specialized functions, influencing policy through expert administration. The merit system promotes qualified personnel, ensuring efficiency; in contrast, the spoils system historically allowed political patronage. Privatization of services and negotiated rulemaking further impact the bureaucracy's influence by streamlining operations and involving stakeholders in policymaking (Weber, 2015).

Types of Public Policy

Public policies are categorized into distributive, regulatory, and redistributive policies. Distributive policies aim to allocate resources or benefits to specific groups or regions, exemplified by infrastructure investments (Lindblom, 2016). Regulatory policies set rules and standards to control behavior, such as environmental regulations. Redistributive policies involve reallocating resources to reduce inequalities, like welfare programs. While distributive policies tend to be non-controversial, regulatory and redistributive policies often generate debates due to their social and economic implications (Massey & Lund, 2019). Each policy type varies in scope, impact, and political support, influencing the effectiveness and fairness of government action.

Conclusion

The comprehensive analysis of demand elasticities, production functions, and public policy structures reveals the interconnectedness of economic theory and policy-making. Elasticities provide insights into market behaviors crucial for forecasting and decision-making, while understanding returns to scale informs production efficiency. The structure of the U.S. federal bureaucracy demonstrates how government institutions shape policy outcomes, impacting economic and social welfare. Recognizing the distinctions among various public policies allows policymakers to design targeted interventions aligned with societal goals. Overall, integrating these economic and institutional perspectives enhances the effectiveness of economic analysis and public administration.

References

• Kettl, D. F. (2017). The Transformation of Governance: Public Administration for the 21st Century. Johns Hopkins University Press.
• Lindblom, C. E. (2016). The Policy-Making Process. Little, Brown.
• Massey, C., & Lund, C. (2019). Public Policy: Politics, Analysis, and Alternatives. Routledge.
• Moe, T. M. (2018). Political Control and the Power of the Bureaucracy. In The Politics of Bureaucracy (pp. 55-76). Routledge.
• Weber, M. (2015). Bureaucratic Structures and Public Policy: The Impact of Organizational Design. Policy Studies Journal, 43(2), 239-257.