2. [30 pts] A giant Economic consulting firm is preparing to move to Austin, hence will bid for a piece of land in Austin, to construct a building that will yield 3 acres of office space. Assume that the expected monthly revenue is $80 million/month (independent of location, for 3 acres office space). Moreover, expected monthly non-land costs (overhead) are $15 million/month and the expected monthly transportation costs are measured as T(x) = 5x (where "x" is the distance to the city center) for the firm. Assume that the consulting firm faces four building options for its office space (each option yields exactly 3 acres of office space): Building Land Size Cost of Building One story 3 acres $10 million /month 3-story 1 acres $20 million /month 5-story 0.6 acres $30 million /month 10-story 0.3 acres $40 million /month Note that the bidding system only accepts bids converted on "per acre" basis, no matter how small/large the desired land is. a. If the consulting firm cannot engage in factor substitution, and has to build a one-story office building, what would be the bid-rent curve per acre? Derive the willingness to pay function and graph the corresponding bid-rent curve locating origin at the center of your graph. Label and solve for all intersection points. b. If the finance firm can engage in factor substitution, and can choose to build facility of their choice (out of the 4 options listed above), what would be the bid-rent curve per acre of land? Derive the willingness to pay functions (per acre) and graph the corresponding bid-rent curves (hint: Draw the merged/max curve) locating origin at the center of your graph. Label and solve for all intersection points. (Hint: Textbook does not have an example of this type, please see class notes.)Office Bid Rent with & without Factor Substitution Question: A nance firm is trying to calculate their bid rent curve for an ofce space. Assume that the expected monthly revenue for one acre of office space is $600 I month. Moreover, expected monthly non-land costs (overhead) are Slim/month per one acre of ofce space and the expected monthly transportation costs are measured as T(x)=x"(3/2) per once acre of office space (since more ofce space means more employees etc.). Assume that the finance firm faces three building options for its office space: Building Cost of 7Building _ne tory 1 acre a. If the finance firm cannot engage in factor substitution, and has to build a one-story ofce building, what would be the bid-rent curve for one acre of office space? Derive the willingness to pay function, and graph the corresponding bid-rent curve locating origin at the center of your graph. Label and solve for all intersection points. b. If the finance firm can engage in factor substitution, and can choose to build facility of their choice (out of the three options listed above), what would be the bid-rent curve for one acre of office space? Derive the willingness to pay function, and graph the corresponding bid-rent curve (hint: merged curve) locating origin at the center of your graph. Label and solve for all intersection points Solution: Derive WTP functions per hectare for each option: Solution to part (a): . WTP, =600 - 100 - 70 - x^(3/2) = 430 - x3/2 For part (b): . WTP AS= [600 - 100 - 200 - x^(3/2)] / 0.25 = 1200 - 4 x3/2 . WTP 10s= [600 - 100 - 350 - x^(3/2)] / 0.1 =1500 - 10 x3/2Notes: WTP ($) -- At any point on the x-axis (miles to center), the highest of the three bid-curves (WTP) is the most $1500 WTP 10s the finance firm is willing to bid for the land available to rent. -- The closer to the center, the more profitable to build up (chose higher story building option) $1200 -- Merge the winning portions of the 3 curves to obtain the equilibrium bid rent curve for the finance firm with factor substitution. $430 WTP AS WTP IS 0 27.3 43 54 (City Center = ( solve for ( solve for (solve for WTP15=0) Distance to city Highway) WTP10s=0) WTP4s=0) center (miles)