Question

Question 2                   Impact of price reduction on revenue

A hardware store in a regional city is well known for its range of gardening tools and building supplies – particularly timber. One year, there is an over-supply of timber, which means that the hardware store must reduce the price of its timber to clear excess stock. For a limited time, the hardware store manager decides to have a timber sale, during which GST of 10% does not apply.

Your task is to determine the consequences of the short-term removal of 10% GST.

The supply and demand equations are given by

Demand Equation:     = 150 − 10aq

Supply Equation:     = 0.044 ² + 3.3bq + 77

where q is the mass of timber (in hundreds of kilograms) ; p is the price of timber in dollars.

1. and b are coefficients to be chosen below.

Steps to complete to undertake the investigation

1. Obtain two random numbers for a and b between 0.1 and 0.9 inclusive. Use the RANDOM key on your calculator.

2. Find the equilibrium price and quantity algebraically, without the price decrease.

3. Update the supply equation to include the removal of 10% GST.

4. Use algebra to find the new equilibrium price and quantity, with the cash-back.

5. Draw a  graph on the same set of axes, the original supply and demand equations (from part 1) and the updated supply equation with the proposed tax removal (part 3).

6. Use your results to complete the following summary table. Round answers to two decimal places, except for total revenue amounts which round to 0 decimal places

Answer 1