EEP141 Problem Set 1 2021 Spring: Due Feb 19th 5PM 1 The Middleman Model Part A In your own words (1-2 sentences each): 1. Briefly describe what a middleman is. 2. Give an example of a firm operating as a middleman and explain why it fits the description. 3. In lecture, we introduced extensions to the basic middleman model. For example, we discussed ”learning,” which suggests efficiency will increase over time and may change how a middleman invests. Name another extension and explain how it adds to the base model. Part B Let’s consider a middleman firm in the business of producing ethanol. Assume that the firm can produce its own corn (the feedstock) or it can purchase corn from third party farmers. The firm processes the corn into ethanol on its own. To maintain consistency with your notes, let’s call our feedstock Xh (in-house) and Xm (third party). Suppose the inverse demand curve is P = 109−2Q and the production function is Q = f (X) = 3(Xh +Xm )2 . The cost of producing corn in-house is Ch (Xh ) = 15 + 2Xh2 . The cost function of a third party producer is 2 . Finally, the cost of processing feedstock from either source is Cp (X) = (Xh + Xm )2 . Cm (Xm ) = 5 + Xm For this middleman, find the: 1. Marginal productivity of the input. 2. Marginal revenue of the output (remeber - this is Q, not X) 3. Marginal outlay Part C First, suppose that the middle man is unable to produce feedstock in-house due to land limitations. He wants to determine the optimal level of Xm . 1. Write down the objective function. 2. Write down the first order condition. 3. Solve for the optimal level of Xm 1 Part D Next, assume there are no restrictions. The middle man wants to determine the optimal levels of Xh and Xm . 1. Write down the objective function. 2. Write down the first order condition. 3. Solve for the optimal level of in-house feedstock in terms of third party feedstock, 2 Xh Xm Hedonics Part A Please answer the following questions in your own words: 1. Provide a short explanation of hedonic analysis. 2. Generally speaking, what does it allow us to estimate? 3. Can we use hedonic analysis to measure people’s willingness-to-pay for clear air through housing market? If yes, provide us with a research design to achieve the goal. Part B Hedonic analysis is applied in housing market a lot. Here we assume houses only differ along four dimensions: 1. House size. This is a continuous varialbe in square feet. 2. Number of bathrooms. This is a discrete variable. 3. Within school areas. This is a binary variable that takes the value 1 for houses that are close to schools and 0 for houses that are far from schools. 4. Yard size. This is a continuous variable in square feet. Further assume that the price of homes is linear in these four attributes. price = α ∗ size + β ∗ bathrooms + γ ∗ school + δ ∗ yard (1) You are given the following data. 1. House 1: size=800, bathrooms=1, school=1, yard=20, price=91,000 2. House 2: size=2000, bathrooms=3.5, school=0, yard=200, price=217,000 3. House 3: size=1400, bathrooms=2, school=0, yard=100, price=149,000 4. House 4: size=1000, bathrooms=1, school=0, yard=80, price=106,000 Questions: 1. Please find the prices of each attribute, i.e. the values of α, β, γ, δ. 2. Now there is a House 5: size=900, bathrooms=1.5, school=1, yard=10. What’s the value of House 5? 2 3 Net Present Value Part A An ethanol processing facility costs $40,000 to construct and will last 6 years (it is constructed in year 0 and runs from year 1 through year 6). It produces 3,000 barrels of ethanol per year and can charge a price of $6 per barrel. If the interest rate is 9%, what is the net present value of this facility? Part B A different ethanol processing facility costs $700,000 to construct but will instead last forever. Every year (starting the year after construction), it produces 10,000 barrels of ethanol and can charge a price of $6 per barrel. At what interest rate would an investor be indifferent between constructing the facility and simply keeping the money? 4 Amber Waves An important part of agricultural economics is making information digestible for people who may not be familiar with the material, including farmers, policymakers, or biologists. Several journals are relatively ”public-facing” in content - intentionally less technical and more accessible to a broad audience. Look through these sites, choose an article (cite it!), and summarize in 1-2 paragraphs. Choices: https://www.choicesmagazine.org/ Amber Waves: https://www.ers.usda.gov/amber-waves/ ARE Update: https://giannini.ucop.edu/publications/are-update/ 3
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