Question One

For the following total-revenue and total-cost functions of a firm:

TR=22Q - 0.5Q²

TC= (1/3)Q³ - 8.5Q² + 50Q + 90

1. Determine the level of output at which the firm maximizes its total profit.
2. Determine the maximum profit that the firm could earn.

Question Two

The coefficient of income in a regression of the quantity demanded of a commodity on price, income and other variables is 10.

1. Calculate the income elasticity of demand for this commodity at income of K10,000 and sales of 80,000 units.
2. What would be the income elasticity of demand if sales increased from 800,000 to 900,000 units and income rose from K10,000 to K11,000?
3. What type of good is this commodity?

Question Three

For the past 10 years, you have been observing the sales of your company since you embarked on an aggressive advertising campaign. You have been recording the amounts spent on advertising and the corresponding sales as follows:

Year	Advert (X)	Sales (Y)
2001	10	44
2002	9	40
2003	11	42
2004	12	46
2005	11	48
2006	12	52
2007	13	54
2008	13	58
2009	14	56
2010	15	60

You would like to determine whether a relationship exists between your two variables of interest and therefore decide to run a regression.

1. Specify the estimation model you will use (the econometric form).
2. Identify the independent and the dependent variables.
3. Use an econometric package of your choice (EViews, SPSS, STATA etc) to estimate the model.
4. From the regression output, report the coefficients, standard errors, t-statistics, probability and R-squared (report the results in a table).
5. Re-write the specified model in (a) with values from the regression results and interpret the coefficients.