It''s a Intermediate Micro Economics course. The goal is to model the compensating change in rents and wages when a sports team improves the amenity value of the city.
Part 1: The residents' indifference curves in the cities of North BEH and South BEH need to be determined as a function of wages and rents. The utility function in both communities is U=CHA Where C= consumption of stuff. Each unit of stuff has a price=1 H= consumption of land A= amenity level of the city The budget constraint is W=C+RH Where W=annual wage R= rent per unit of land The nice thing about this setup is that because C and H get equal weight in the utility function, the expenditure on each is the same. North BEH has a football team, South BEH does not. Therefore the amenity level of North BEH is 2, and the amenity level of South BEH is 1. The utility level of both cities is 1.
Find the indifference curves for both North BEH and South BEH as a function of W and R.
Sketch them both on a graph. Note: no calculus is needed for this.
All the calculus would do is tell you that the two expenditures are equal. Note further that the answer should NOT have H, C or U in it. It should only have W as a function of R.
Part 2: Find the zero-profit line for the two communities. Industry in each city produces output for a worldwide market using a production function with land and labor (L) Q=L1/2 H1/2 It turns out that if you do the calculus, maximizing profits subject to the appropriate constraints, that the average cost of production, AC, as a function of the input prices, has the form AC=2W1/2 R1/2 In a competitive environment we know that profit will be zero, which is the same thing as saying that the price of output equals average cost.
In the world market, the output price is taken as given by the firm. Suppose the price is 10.Using these facts, find the firm indifference curve between W and R. Sketch this function on the same graph similar to part 1.
Note: No calculus is needed. The calculus would have only told you what the AC function looks like. Again, W and R should be the only variables in your answer.
Part 3: Using the answers in part 1 and 2, algebraically find the W* and the R* that will occur in the North BEH and South BEH. Interpret between the wages and rents in the two communities.
Part 4: There are 1 million people in each city. Find the willingness to pay(for the city as a whole) for the football team.