Where , are the parameters to be estimated though will remain equal to 0 as we do not want an intercept in order to find the variable cost per baguette, P is the price of each baguette, Q is the quantity produced, and is a random error term. Summary output tables of each model are attached at Exhibits 1 and 2, respectively.
I used a multiplicative exponential regression model because in such a model, the coefficients are the respective elasticity, and I was trying to find the price elasticity of demand for the baguette. The multiplicative exponential model in linear form is:
Ln(Total Sales) = 8.82 – 1.491lnP (.112) (.177)
The numbers in parenthesis are standard errors, and is the standard error of the term. Overall, this model explains approximately 79.8% of the variation in the natural log of total sales of baguettes.
I also used a linear regression model because I wanted the each set of data to remain in its current respective unit, rather than find the natural log of each. The linear regression model in linear form is:
Total Variable Cost = 0 + 0.601Q (0) (0.002)
The numbers in parenthesis are the standard errors, and is the standard error of the term. Overall, this model explains approximately 100% of the variation in total variable cost of baguettes.
You asked me to find the optimal price at which to sell our baguettes. To find the optimal price, I began by using the optimal markup pricing factor equation given below:
Optimal Markup Pricing Factor =
Once I plugged in the price elasticity of demand of -1.49127, I solved the equation to receive an optimal markup pricing factor of 3.036. In order to use this to find the optimal price per baguette, I need to find the marginal cost of supplying a single baguette.
In order to find the marginal cost, I set the intercept to 0 in my linear regression model because I only wanted to find the variable cost, this way I would not have a fixed cost (which we are ignoring in this analysis). The results displayed the variable cost per each baguette produced as about $0.6 per baguette. Using the optimal markup pricing factor and the variable cost of supplying a baguette, I multiplied the two to find that the optimal price per baguette is about $1.82.
Along with finding the optimal pricing of the baguette, you asked me to find the optimal output level. At the optimal output level, we would maximize profits. When production is set at 10% above expected sales, our profit function looks like this:
In looking at the profit function, I noticed that it is a linear function. Therefore, I concluded that the optimal output level is infinite. The greater Q produced, the greater the profits will be, so I would advise producing as many baguettes as possible. Eventually, there would be a maximum point of production our company will reach though, like maximizing the output of our factories. In conclusion of this analysis, I have found that the optimal pricing is $1.82 per baguette, and the optimal output is infinite.
For example, in the data you gave…