Problem Set 4

Urban Economics, Fall 2023, Problem Set #4 Due Tuesday, November 7, at 11pm, online on Brightspace show your work no late problem sets, one single file submissions only Word, Excel, or PDF formats only (1) Multiplier a) Assume a city knows that its long-term income multiplier equals 2.9. What is the implicit m ? (be precise to 4 decimals) b) True or false? Do not explain. If ΔX>0 and m=0, the change in income Δ Y will always be zero too. c) Assume m=0.4 and ΔX=20,000. If ΔX, the initial impulse, occurs in time period zero what is the income change ΔY after period four? What is the income multiplier after period four? (be precise to 4 decimals) (2) Input-Output Tables Assume the following Input-Output Table depicts the inter-industrial relations of a city where people drink a lot of beer. Producers Inputs Steel Beer Local Households (labor) Exports Total Steel 30 20 10 0 200 Beer 30 60 20 240 10 Local 10 10 40 80 30 Labor 150 80 80 40 0 Imports 40 30 10 40 0 Show the corresponding Input Coefficient Table (note, imports and export do not have to be identical). (3) Input-Output Tables and Impact Use the Input-Output Table above and suppose the beer industry enjoys a $100 increase in exports. Show the overall income increase in the steel industry, in the beer industry, for local businesses and the increase in labor income after round 2 (time periods); assume the initial impulse happens in round zero. Note that this Table also shows intra-industrial trade. For instance, the steel industry also needs steel as an input. If the initial income impulse is $100, what is the overall income increase in Round 1, what is it in Round 2? Add up the all three numbers and calculate the overall income increase (This question requires some careful calculations). In these two rounds, how much has the initial impulse multiplied?