Practice calculations and problem-solving techniques

Practice Calculations

To compute the elasticity for a variable, we must calculate the degree to which demand changes for every unit change in the variable. The first step is to calculate the current level of demand:

20Px + 5.2I + .2A + .25M

This can be calculated in Excel using the values given in the base example. The current demand therefore is 17,650. To calculate the elasticity associated with a variable, the variable should change by one unit and then the change in demand would be noted. The formula for determining elasticity is to take the change in the demand/change in variable. So for example, if we want to test P, we can it by $.01. Demand becomes 17,608. The price elasticity of demand therefore is:

(17608 -- 17650) / (501 -- 500) or -42/1 = -42, meaning that for every penny the price increases, 42 fewer units will be sold. We can see that the elasticity is the same as the numbers in the formula. So we know that the elasticity for Px is +20; elasticity for I is 5.2; elasticity for a is .2 and elasticity for M. is .25. These can be tested mathematically in Excel using the formula.

2) a recession would increase the unemployment rate. Wages are the closest proxy in this equation to the unemployment rate. Although wages are relatively sticky, the average wage in the region should decrease as the unemployment rate increases. If the average wage in the region decreased 10%, it would fall to $4,950. Demand under this scenario would fall to 14,790, which is a decrease of 16.2%. Thus, the company should be very concerned about the impacts of a recession. Sales are expected to decline significantly if the average wage in the area is reduced.

3) to determine if the firm should increase market share by lowering the price, total revenue must be considered. At $5.00, the firm sells 17650 units for total revenue of $88,250. At $4.99, the firm sells 17,692 units for a total profit of $88,283.08. Thus, the firm gains addition revenue by lowering its price to sell more units, at least to a point. At some point, lowering the price will result in a decrease in total revenue.

4) to calculate the portion of sales that is reliant on the independent variables, set the variables to zero. The sales remaining will be the portion that is not dependent on these variables. The base market is negative in total, so these variables determine all of the sales. To determine how much each individual variable contributes, they can be set to zero one at a time. Thus, there are 38,650 potential sales available if the price is zero. If the competitor's price is zero, the company will still receive 5650 sales in theory. These 5650 sales are not price dependent. So 14.6% of the total market is not price dependent.