# August 2008 Final Exam Answers - 1 Answers August 08 Exam...

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1 Answers: August 08 Exam Question 1 (a) First solve for the equilibrium intersection of supply and demand. This intersection tells us how much output will be produced if the city lets the market reach its own equilibrium, with no growth control policy. MC = 6000 + 50u = P = 43,500 – 200u so 250u = 37,500. Thus u = 150. Since there are 50 acres of land in the land supply and a minimum lot size = 0.25 acres, the zoning regulation is limiting total output to no more than 200 units. This is more than the unregulated equilibrium output (150), so the zoning regulation is non-binding. The supply/demand diagram should show intersection of supply and demand at u = 150, P - \$13,500. Total revenue is \$2.025 million and capital cost (area under MC from 0 to 150) is \$1,462,500. Total land cost = \$2,025,000 - \$1,462,500 = \$562,500 (rent = \$11,250 / acre). The industry isoquant/isocost diagram should show the u = 150 isoquant with tangent isocost line (slope = \$11,500). Given the absence of a binding zoning constraint, factor substitution can operate ensuring the isocost/ isoquant tangency condition. The C-axis coordinate of the tangency point should be \$1,462,500 and the L-axis coordinate should be 50 acres. The C-axis intercept of the tangent isocost line should be at total revenue = \$2,025,000 since with an unregulated market there is zero economic profit. The firm isoquant/isocost diagram should show the isoquant for u = 5 (the firm’s fixed output as given in the question. There are 30 firms since total output = 150. Thus each firm’s land input is 50 / 30 = 1.67 acres. Each firm’s capital input is \$1,462,500 / 30 = \$48,750. These inputs should be shown as coordinates of the isoquant/isocost tangency point. The C-axis intercept of the isocost line is the firm’s total revenue (\$2,025,000 / 30 = \$67,500). (b) With this higher position of the demand curve the zoning regulation is binding. The intersection of supply and demand would be at u = 250, but the zoning does not allow output to go above u = 200. The supply/demand diagram should show a vertical region of the supply curve at u = 200. Equilibrium price is at \$28,500, so total revenue = \$5.7 million. Total capital cost = area under MC from u = 0 to u = 200 = \$2.2 million. Thus

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2 total land cost is \$5.7 million minus \$2.2 million = \$3.5 million (rent = \$3.5 million / 50 = \$70,000 / acre. The industry isoquant/isocost diagram should show the industry producing on the u = 200 isoquant at the point where L = 50 acres, C = \$2.2 million. A non-tangent isocost line should connect this point to \$5.7 million on the C axis, since there is zero economic profit with the zoning policy (no barrier to competition). The non-tangency condition is due to no factor substitution with the zoning policy in effect (industry cannot temporarily use less than 50 acres of land which would create excess supply, leading to lower rents until tangency is reached). The firm’s isoquant/isocost diagram should show the u = 5 isoquant, this time with each
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