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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 x is defined as x = 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* × 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** Q* In
Transcribed Image Text: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 x is defined as x = 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* × 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** Q* In
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