Consider the perfectly competitive market for one good. That is, both consumers and producers are price takers. The demand function is given by QD = ?aP +b, where a > 0 and b > 0 are real numbers and P is the market price. The supply is given by QS = cP, where c > 0 is a real number. Assume the government introduces a per-unit tax,? , that is paid by the producers.
1. (2 points) Suppose that a = c = 2 and b = 10. Derive an expression for the tax revenue as a function of the per-unit tax ? . 2. (3 points) Sketch the graph of the tax revenue. That is, plot the tax-revenue on the vertical axis (”the y-axis”) against the per-unit tax, ? , on the horizontal axis (”the x?axis”). Recall that ’sketching a graph’ involves: find the intercept with the y-axis, the intercepts with the x-axis and the shape of the graph. 3. (6 points) Repeat part (1.) and (2.) without assuming specific values for a,b and c. Recall that ’sketching a graph’ involves: find the intercept with the y-axis, the intercepts with the x-axis and the shape of the graph. Some of your answers might dependent on the parameters a, b and c.