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ECON2010 Question 1 The production of potato chips (y) requires two inputs: potatoes (p) and oil (o). The production function is given by y = p 1 2 o 1 2 . The market of potato chips is competitive. The market demand for potato chips is given by P(y) = 12 − y where P(y) is the market price when the market output level is y. In addition, every producer takes pp, the price of potatoes, and po, the price of oil, as given. You may assume that po = 1 throughout this question. (a) (This part is here to simplify your work later. If you prefer, you can solve parts (b) to (d) first before returning to part (a).) Find the marginal cost of producing y units of potato chips in terms of pp, the price of potatoes. (Hint: Feel free to copy anything from the answer to the last tutorial exercise.) (b) Suppose pp = 1. Find the marginal cost of producing y units of potato chips. (c) Given pp = 1, find the market price and market output of potato chips. Can you determine the output level of each individual firm? Why or why not? (d) The government, in an attempt to reduce obesity, wants to reduce potato chips consumption by putting a per-unit tax of t on potato chips. What should be the value of t if the government wants to reduce potato chips consumption to half of the market output in (c)? (e) Instead of taxing potato chips, this government decides to tax potatoes. It is putting a per-unit tax of t on potatoes. What should be the value of t if the government wants to reduce potato chips consumption to half of the market output in (c)?
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