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# Answers June 08 complete - Answers June 2008 Question 1 a...

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Answers June 2008 Question 1 a) Each of the following points is worth ½ a mark, except for the diagrams which are worth 1 mark each, for a total of 8 marks: A brief description of the physical layout of the City. No factor substitution for all firms. No consumer substitution for all residents. ZEP of manufacturing firms determines the position of their bid rent curve. Freight costs determine the slope of manufacturing bid rent curve. ZEP of housing firms determines the position of their bid rent curve. Housing price function determines the slope of the residential bid rent curve. Equilibrium requires land to be rented to the highest bidder. Equilibrium requires labour supplied to equal labour demanded. Open-city model assumption – the city is one of many in a nation, to which any of the residents may costlessly move to obtain the exogenous level of utility. Land market diagram showing the bid rent curves with proper labels. (1) City map indicating the distribution of land and land use boundaries consistent with the land market diagram. (1) Labour market showing supply, demand, and equilibrium wage and population. (1) b) The business bid rent function is derived from the zero economic profit condition: total revenue = total cost. Total revenue per firm is the firm’s output (200 bicycles / month) times the exogenous output price (\$190) = \$38,000. Total cost is the sum of capital cost (\$1000), labour cost (10w), freight cost (\$10 times 200x) and land cost L times R b (all per month). Given that L = 1 hectare, the zero-economic profit condition can be rearranged to give us R b as a function of x and w: R b = 37,000 – 2,000x – 10w. The BRF is linear in x since there is no factor substitution. For every mile that a firm relocates away from the port, freight cost increases by \$10 times 200 = \$2000. To maintain zero economic profit, land rent must decrease by that same \$2000. (4 marks) c) x 1 (w) = 24 – w/100. This is obtained by equating R b and R r as must be the case at the business / residential boundary x 1 . (3 marks) d) x 2 (w) = –8 + w/100 This is obtained by equating R r and R a as must be the case at the residential / agricultural boundary. (3 marks)

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e) Parts (c) and (d) give us two equations in x 1 , x 2 , and w. A third equation can be obtained from the density relationships given in the question. We are told that each manufacturing firm has one hectare as its land input and 10 workers. Thus employment density is 10 workers per hectare. We are also told that each housing firm has 2 hectares as its land input, and also that its 10,000 sq. ft. output is divided among ten households, each renting 1000 sq. ft.; thus there are 10 households on every 2 hectares of land, so residential density is 5 households per hectare. Given that employment density is two times the residential density, we know that the general equilibrium residential land area must be two times the business land area. Since the north-south dimension is common to both business and residential land areas, it would then follow that the residential area’s east- west dimension is two times the business area’s east-west dimension.
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