Demand and supply calculations

Demand and supply calculations

1. The data in Table 5.3 is provided in the Excel file MBA730_New Use this data to replicate the results in Table 5.4. Report your results and note any discrepancies with the text.

Solution

From the computation and analysis output, we have six independent variables that were used in forming the multiple regression model. These variables include; price(P), Advertising(A), Competitor price(PX), Income(Y), Population(Pop) and Time(T). The six variables had coefficient as follows -122.607,5.838,29.867,2.043,0.030,2.15 respectively.

The coefficient of determination=R²=87.1% with the corrected coefficient of the determination being R²=85.2%. The F-statistic was 45.16 with the standard error of estimate being 65.584.

2. Now use the data from Table 5.3 to estimate a multiplicative demand function for Mrs. Smyth’s frozen fruit pies. Report your parameter estimates and regression statistics for the multiplicative model.
3. Describe the statistical significance of each of the independent variables included in Mrs. Smyth’s demand equation. Interpret the coefficient of determination and F statistic for the multiplicative model.

Solution

Price-decreased costs regularly lead to reduced production, and increases in production normally result in a bigger supply. Nevertheless, the supply of different goods responds differently to demand, with the demand for some goods becoming less price reactive than others.

Inelastic pricing suggests a poor effect of the market on demand

Marketing -will boost market awareness and perceptions of your product’s benefits, and maximize the number of consumers likely to purchase your product at the right price. In the end, advertisement influences competition by creating a customer appetite for a product or brand.

Rivalry -determines the price of the marketplace and the more the product is in demand (which is the rivalry between buyers), the greater the price the consumers are willing to pay and the more profits a manufacturer can earn. Greater vendor demand results in lower retail costs for the items.

Cash flow-The impact that tax has on the quantity of a commodity that buyers are eager and able to purchase depends on the type of products we are talking about. In other words, the market price will increase for these products as the income increases; if the output decreases, the cost of production will decrease.

Demographic-As the population continues to grow, demand for goods and services will increase. The more people there are, the more wishes and expectations are expected to be met. The market is influenced not only by the size of the economy but also by the demographic structure.

Time-This means that the price elasticity of demand largely depends on the time it takes for buyers to adapt themselves to new commodity prices. The greater the time cycle, the greater the market price elasticity. That is how customers are accustomed to a rise in prices or new products over some time.

1. Compare the statistical properties of your multiplicative model with the linear model. Which fits the data better? Explain why.

Solution

There is a continuous relationship in the multiplicative model between the input variables and output variables. The independent variables aren’t that strongly correlated. The results are chosen from the population, individually and automatically. Residuals will usually be spread with an average of 0 and variance с whereas the line helps to reduce the number of residuals in linear models Square variations between observable values (Y values) and expected values (Regression equation determined values). The axis of regression traverses the mean of the X values (x) and the mean of the Y values (y). The multiplicative model suits the results well in this situation since the independent variables are not so closely associated with each other. The Reviews

1. In the multiplicative model perform a statistical test to determine whether demand is elastic, your competitor’s product is a substitute, and if pies are a normal good at the 95 percent confidence level.

Solution

Because in this case, the F-statistics is 45.16, we find that the p-value is 0.45. Because 0.45 is greater than 0.05, we will not dismiss the null hypothesis and assume that there is ample proof of a positive association between the dependent variable and the independent one.

1. What is your estimate of the price elasticity of demand, advertising elasticity of demand, income elasticity of demand, and cross-price elasticity of demand in the multiplicative model? Compare these elasticity estimates with the corresponding elasticities in the linear model when calculated at mean values for each variable.

Solution

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1. Using the linear model, what is the expected value of next quarter’s unit sales in the Minneapolis-St. Paul, MN market? Use the value of each independent variable for the last period in the MN market for this forecast. Derive the 95 percent confidence interval for next quarter’s actual sales in the Minneapolis- St. Paul market.

Solution

Dallas and Los Angeles -2007-3

demand curve = Q= 529774-122607P

when p=0, Q= 529774 and when Q=0, then p= 4.3. advertisement, relative price, population, income, etc all held constant.