# Urban Economics Problem Set #5

**Urban Economics**

**Problem Set #5**

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__Question 1__

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.

Equation 1 Ln(profit) | Equation 2 Ln(profit) | |

Temperature (in degree Celsius) | 0.402 (6.62) | 0.302 (6.99) |

(Temperature)2 (in degree Celsius) | -0.009 (4.09) | |

Rainfall Harvest (in milliliters) | -0.435 (-2.99) | -0.455 (-3.04) |

Trend | 0.021 (6.66) | 0.022 (6.36) |

R2 | 0.88 | 0.86 |

- a) Which of the two equations do you prefer? Why?
- b) Refer to Equation 1 and calculate the profit maximizing temperature. Show your

work.

__Question 2__

Assume there are three farms in a county growing corn in a perfectly competitive market.

The overall global market supply of corn is given by QS=P. The demand function equals QD=100-P. The marginal cost functions for the farms are given by MC1=48+Q, MC2=46+Q and MC3=42+Q. Assume there is no fixed cost of production.

- a) Calculate the overall market equilibrium quantity and the corresponding market clearing price.

- b) How much corn does each farm produce?
- c) What is each firm’s annual profit?
- d) Assuming a discount rate of 4% and a profit growth rate of 1.5%, what is the land of each firm worth?

- e) Now assume, due to better climatic conditions, marginal cost for each firm falls by $2. Calculate the new marginal cost functions, quantities, profits and the new land values assuming the same discount rates as under (d). What was the sum of the tree land values before and after the change?

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