Question: An economy is populated by N identical consumers. They consume two goods X and Y. Utility is given by U = In(X) -+- In(Y)

An economy is populated by N identical consumers. They consume two goods X and Y. Utility is given by U = In(X) -+- In(Y) and each consumer has an income of 800. Product X is produced by M firms operating on a perfectly competitive market. The production function for each firm that produces X is given by X = KO5 where K is the only input factor in the production of X. K is bought by the firms on the factor market at the price of 10. Fixed costs are 1000 for each firm. Taken together, the M firms sell 10000 units of good X on the market. There are also 20000 units of good Y sold by the Z number of firms who produces Y. a. How many firms M are producing good X, what is the price of good X and how many consumers N are there? b. What is the market demand function for good X, and the market price elasticity of demand c. Now, the government start taxing the producers of good X so that they have to pay a tax of 200 per units sold. How will this affect the price of good X and the number of firms producing X in the long run?

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