hw4 - C = 1600 + 40 Q + 2 3 Q 3 / 2 He sells his output to...

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ECONOMICS 331 Mathematical Economics Kevin Wainwright Homework Assignment 4 Q d = kP ² ( ²> 0) Q s = c ( P T 0 ) are the demand and supply curves for a commodity whose price is P. T 0 is a sales tax imposed by the government on sales of this commodity. (a) Compute the price elasticity of demand and the price elasticity of supply of this com- modity. (b) Find an expression for P/ T 0 where P is the equilibrium price in this market. (c) Show that 0 < P/ T 0 < 1 . (d) Total tax revenue collected by the government is R = T 0 Q. Find an expression for R/ T 0 . [2] Consider the operator of a small newsprint production plant. He has f xed costs of $1600 per day for property taxes, interest on debt, etc., and has additional costs that vary with the amount Q of newsprint he produces. His total costs per day are given by
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Unformatted text preview: C = 1600 + 40 Q + 2 3 Q 3 / 2 He sells his output to local newspaper publishers and the price he obtains depends on how much he tries to sell. Let the demand curve he faces be P = 100 + 512 Q 1 / 2 (a) What are his average and marginal costs of production expressed as functions of Q ? (b) What are his total and marginal revenues expressed as functions of Q ? (c) How much output per day should he produce if he expands production just to the point where marginal revenue equals marginal cost? What pro f t if any will he make in $/day? (hint: substitute X = Q 1 / 2 into the equation you have to solve, determine X , then Q ) 1...
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