EC3317: SPRING 2022 MARIS GOLDMANIS ASSESSED ASSIGNMENT 1 1. Consider a small, isolated island with a coconut oil indust

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Ec3317 Spring 2022 Maris Goldmanis Assessed Assignment 1 1 Consider A Small Isolated Island With A Coconut Oil Indust 1 (70.52 KiB) Viewed 81 times

EC3317: SPRING 2022 MARIS GOLDMANIS ASSESSED ASSIGNMENT 1 1. Consider a small, isolated island with a coconut oil industry and three villages. Coconut oil can be produced at a constant per-unit cost of 50 pesos per liter. All the oil is sold in the villages, and due to the close proximity of the villages to each other, the retail price in all three villages must be the same. The three villages' demand for coconut oil is given by the following indirect demand functions (wirere , is the amount of coconut oil (in liters) consumed by village i and P, is the price in pesos per liter) that the people living in village i are willing to pay for the marginal liter): P.(Q1) = 210-To 2. P.(Q:) = 400-23 P.(Q:) =600-23- The production of coconut oil creates environmental damage, mostly via deforestation associated with growing coconut trees, but also via water and air pollution from chem- icals used in the oil extraction industry. The marginal damage due to deforestation is MDF(Q) = 10 + LQ (pesos per liter of coconut oil produced), whereas the marginal damage due to pollution is MDP(Q) = 10 (pesos per liter of coconut oil produced) (a) 15 marks Find the aggregate demand function for coconut oil, linking aggregate quantity to market price P. Don't forget the "kinka" that arise form the fact that not all villages are demanding oil at all prices (b) 5 marks Find the aggregate marginal damage function. (c) 5 marks Find the level of coconut oil production that maximizes total surplus in the coconut oil market taken in isolation (ignoring the effects of environmental damage). Call this output level Q (d) 20 marks. Find the socially optimal (truly efficient) level of coconut oil production (Q"), which maximizes total surplus after accounting for environmental damage. (e) 10 marks Suppose coconut oil on the island is produced by perfectly competitive producers. What price will be charged (P) and how much oil will be produced (Qc)? (1) 10 marks How does the competitive output level Qe compare to the benchmark levels Q and Q? Why? (8) 10 marks Suppose the government wants to implement the socially optimal level by introducing a per-unit tax on coconut oil production. Determine te, the level of tax (in pesos per liter) that achieves this goal. (h) 5 marks What will be the competitive equilibrium price after the tax computed in part (g) is put in place? (1) 10 marks Compute the quantities of coconut oil consumed before and after the tax in each village separately. 6) 10 marks Based on your answer to part (i), which village was the most affected by the tax, and why?