Ps5a Fall2019 - Problem Set 5 Answers Karl Storchman PDF

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Problem Set 5 Answers
Karl Storchman...

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Urban Economics Problem Set #5 Due: NYU Classes, Monday Dec 9, 11.55pm You can submit only one single file (only Word, Excel or PDF) Once submitted, a problem set cannot be recalled anymore show your work!

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.

Temperature (in degree Celsius) (Temperature)2 (in degree Celsius) Rainfall Harvest (in milliliters) Trend

Equation 1 ln(profit) 0.140 (1.62) -0.003 (-1.49) -0.335 (-1.09) 0.021*** (6.66)

R2 0.85 T-statistics in parentheses; Significance levels 1% (***), 2% (**), 5% (*)

Equation 2 ln(profit) 0.302*** (2.99)

-0.455*** (-3.94) 0.022** (2.36) 0.91

a) Which of the two equations do you prefer? Why? Equation 2 is better because all variables are significant. In Equation 1 only trend is significant. Also, Equation has a higher R2 value b) Refer to Equation 1 and calculate the average trend-induced inflation rate of nominal profits. (equal to the coefficient, i.e., roughly 2.1%) The rule of thumb is: the coefficient is equal to the percentage marginal effect = 2.1% More precise is e0.021 = 2.12% c) Refer to Equation 1, disregard the low significance levels, and calculate the profitmaximizing temperature Topt = 0.140/(2*0.003) = 23.33

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. P=50, Q=50 b) How much corn does each farm produce? since the price is P=50 each firm will find the profit maximizing quantity where 50=MC Firm 1 à 50=48+q à q1=2 Firm 2 à 50=46+q à q2=4 Firm 3 à 50=42+q à q3=8 c) What is each firm’s annual profit? The profits are the area between P and MC, ∏1=0.5*(2*(50-48))=2 ∏2=0.5*(4*(50-46))=8 ∏3=0.5*(8*(50-42))=32 d) Assuming a discount rate of 4% and a profit growth rate of 0.5%, what is the land of each firm worth? NPV1=2/(0.04-0.005)=2/0.035=57.14 NPV2=8/(0.04-0.005)=8/0.035=228.57 NPV3=32/(0.04-0.005)=32/0.035=914.29 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 and growth rates as under (d). What was the sum of the three land values before and after the change? Lower the constant term of each MC function by one and set equal to the price Firm 1 à 50=46+q à q1=4 Firm 2 à 50=44+q à q2=6 Firm 3 à 50=40+q à q3=10 ∏1=0.5*(4*(50-46))=8 ∏2=0.5*(6*(50-44))=18 ∏3=0.5*(10*(50-40))=50 NPV1=8/(0.04-0.005)=8/0.035=228.57 NPV2=18/(0.04-0.005)=18/0.035=514.29 NPV3=50/(0.04-0.005)=50/0.035=1,428.57 Before: 57.14+228.57+914.29=1,200.00 After: 228.57+514.29+1,428.57=2,171.43

Question 3 A firm that produces metal occupies four hectares of land. The firm produces 10 tons of output per day and sells its output at a price of $240 per ton. The firm does not engage in factor substitution as the price of land changes. Intra-urban transportation is on trucks, with a unit cost of $12 per ton per mile. The firm’s non-land cost is $560 per day. The firm exports its output via circumferential highway (i.e., beltway around the city). (a) Draw the firm’s bid-rent curve for land for different distances from the beltway, from a distance zero to five miles. (b) What is the bid-rent at the beltway? What is the slope of the bid-rent function? Show your work. ANSWER a. The firm’s bid-rent curve is linear (because of fixed factor proportions) and decreasing in the distance to the beltway. b. The bid rent at the beltway is $460 per hectare (i.e., its revenue 2,400 minus 560 nonland cost divided by 4 hectares) and the slope of the bid-rent curve is $30 per mile, computed as ($12 x 10) / 4.

(4) Choice of Public Good Assume there are 7 people (A, B, C, D, E, F, G) in a small village. The following Table reports their preference regarding the size (in hectare) of a planned park Person

A

B

C

D

E

F

G

Preferred Park Size

12

1

0

10

2

666

1220

(a) Assuming the village finds the “optimal” park size by employing the majority rule. How big will the park be? (b) Using your answer from (a), if the per hectare cost of parkland equals $60, what is the “tax share” of each person? Answer:

(a) sort them by preferred size. The median preference is 10. Thus, A will get his/her will. (b) Total cost will be 60*10=600. The equal tax share of each person will be $600/7=$85.71...