In: Economics
Beatriz enjoys writing and uses a large amount of paper. Currently, paper costs $2.00 for 100 sheets. The formula for her demand curve is S=525−50PS, where PS is the price of 100 sheets and S is the number of packages of 100 sheets. The governor of her state has proposed taxing paper at the rate of $1.50 for each 100 sheets. Assume this policy would increase the price of paper to $3.50 (including tax). Draw Beatriz's demand curve. Instructions: Use the tool provided "Demand" to plot Beatriz's demand curve. The x-axis represents S, and the y-axis represents PS. a. Compute the change in her consumer surplus for the proposed tax increase. Instructions: Round your answer to 2 decimal places. Include a negative sign if necessary. $ b. How much revenue will the government raise by taxing Beatriz? Instructions: Enter your answer as a whole number. $ What is the combined change in government revenue and consumer surplus? Instructions: Enter your answer as a whole number. Include a negative sign if necessary. $ Does the new tax raise enough revenue for the government to compensate Beatriz for her loss? Yes No
Answer:
The objective of the following analysis is to consider the demand function for the sheets and evaluate the change in the consumer surplus after imposition of tax at the rate of $0.50 for every 100 sheets, determine the revenue earned by the government from the tax and assess if the revenue raised by the tax is enough to compensate for the loss in consumer surplus.
a)
It shall be noted that the demand function is given by:
Where,
: Price per 100 sheet of paper
: Number of Bundle purchased each with 100 sheets
On plotting the demand curve, the result obtained is:
The inverse demand function is:
The total cost of the paper used is:
The marginal cost of the paper is:
Thus, the equilibrium condition is given by:
This implies,
Thus, the equilibrium quantity is
The equilibrium price is:
The Pre-tax consumer surplus is given by the area of the triangle enclosed between the downward sloping blue line and (Demand curve) and Orange line (MC = $2):
When a tax of $0.5 for each 100 sheets is imposed such that new price is $2.50 per 100 sheet
The post-tax inverse demand function is unchanged and is given by:
The new total cost of the paper is:
The new marginal cost of the paper is represented by the green horizontal line as shown in the graph:
Thus, a new equilibrium is given by:
The Post-tax consumer surplus is given by the area of the triangle bounded by the downward sloping blue line (demand curve) and orange line (MC’=$2.5):
Thus, the decrease in consumer surplus is:
b)
The Post-tax equilibrium quantity is, implying that there are 400 bundles of 100 sheets each.
The revenue earned by the government from imposing $0.5 per 100 sheets is:
Thus, the revenue collected by the government falls short by $6.25 (indicated by a small red-triangle in the graph) vis-a-vis in economic loss faced by the consumer, which is a decrease in consumer surplus to the extent of $206.25.
Thus, the new tax does not raise enough revenue for the government to compensate for economic loss.