Urban Economics Problem Set 5: No Late Problems Sets You Can

Urban Economicsproblem Set 5no Late Problems Setsyou Can Only Submit

Assume you run regression where you explain vineyard land profits as a function of temperature, rainfall and a time trend. The table below reports the results of two different models. The dependent variable is the natural logarithm of profits. Which of the two equations do you prefer? Why? Refer to Equation 1 and calculate the profit-maximizing temperature. Show your work.

Paper For Above instruction

The primary task in this assignment involves evaluating two regression models predicting vineyard land profits based on climatic factors and a time trend. The goal is to determine which model is preferable and to utilize the preferred model to calculate the temperature that maximizes profits, emphasizing the application of economic and statistical principles in land use and climate data analysis.

The comparison of models requires examining coefficients, statistical significance, and model fit. The more suitable model will generally be the one that better explains the variability in profits, exhibits interpretability, and maintains statistical coherence. The calculation of the profit-maximizing temperature entails deriving the vertex of the quadratic function represented by Equation 1, by setting the first derivative of the logged profit function with respect to temperature to zero.

Using the given coefficients, the profit-maximizing temperature \( T^* \) is obtained by solving the first-order condition derived from Equation 1, which includes the linear term for temperature and the quadratic term for temperature squared. This involves taking the derivative, setting it equal to zero, and solving for \( T \).

Overall, this analytical exercise combines regression evaluation with calculus to enhance understanding of how climatic variables influence economic profits in vineyard land management.

References

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