4. Consider a perfectly competitive market in which a tax of to ≥ 0 is collected from sellers for each unit sold. Price and quantity are determined by the following supply and demand functions: - Qd 1000-20P - Qs =-200+100(P-to) a. Write down the matrix equation Ax = b that describes the equilibrium combination of price and quantity when a is defined as a = particular, what are A and b? b. Use Cramer's rule to find the function that relates the equilibrium quantity (Q*) to the perunit tax(to). c. Write down the equation that describes total tax revenue as a univariate function of to. Hint: by definition, TTR = Q* x× to. d. Find the first and second derivatives of the total tax revenue function. e. How large would the tax need to be in order to maximize total tax revenue? P** . In

4. Consider a perfectly competitive market in which a tax of to ≥ 0 is collected from sellers for each unit sold. Price and quantity are determined by the following supply and demand functions: - Qd 1000-20P - Qs =-200+100(P-to) a. Write down the matrix equation Ax = b that describes the equilibrium combination of price and quantity when a is defined as a = particular, what are A and b? b. Use Cramer's rule to find the function that relates the equilibrium quantity (Q) to the perunit tax(to). c. Write down the equation that describes total tax revenue as a univariate function of to. Hint: by definition, TTR = Q x× to. d. Find the first and second derivatives of the total tax revenue function. e. How large would the tax need to be in order to maximize total tax revenue? P** . In

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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