ECO 507
Managerial Economics
Satyajit Ghosh
Fall 2022
Assignment 1
Due on October 8 in Brightspace Dropbox
Show and explain all calculations. Provide detailed economic reasoning. Excel is to be used only in 1 (a, b, c), 2(c) and 5. Answers must be submitted in a word file or a single PDF, with Excel attachments. Work independently.
The domestic demand and supply function for oil for a small country are given by: Qd = 210 – 1.5P and Qs = – 140 + 2P, where P is the price per barrel and Qd Qs are the quantities in million barrels.
(a) Use Excel to calculate quantity demanded and quantity supplied for P = $70, 75,80….140 (in $5 increments). Determine the equilibrium price and quantity in absence of any oil import.
(b) Assume that OPEC can sell unlimited quantity of oil at $80 per barrel. Using your calculations in (a), determine the equilibrium price, amount of domestic consumption, quantity supplied by domestic producers and the amount of oil import. (Assume that at a given price, the amount of import is the gap between domestic demand and domestic production.) Explain.
(c) Now, suppose the country’s government imposes a limit on the amount of oil that can be imported from OPEC at their price of $80. Given that the limit is set at 35 million barrels, use Excel and the spreadsheet created in part (a) above to calculate the aggregate supply of oil that includes the domestic supply and the import from OPEC. Calculate the domestic price for oil, domestic consumption, and domestic production. Explain.
(d) Algebraically determine the results that you calculated in (a), (b) and (c) above using Excel. Explain.
(Note: (a)-(c) should be answered using Excel only; (d) should be answered using only algebra)
(26 points)
2. The Taxpayer Assistance Center (TAC) provides taxpayer assistance to help in the preparation of individual tax returns. The amount of assistance (A) that can be provided is a function of the number of professional accountants (P) and trained tax preparers (T) that are employed. The function is given by:
A = 500P +200T +50PT
(a) TAC has budgeted $700,000 for a new office to pay for the accountants and the tax preparers. It pays an accountant $100,000 and a tax preparer $50,000. Using the Lagrangian multiplier approach calculate the optimal staff combination that can maximize the amount of tax assistance. Determine the optimal amount of assistance provided by TAC. Explain your calculations.
(20 points)
(b) Calculate the marginal cost of providing additional assistance. Explain your answer.
(6 points)
(c) Using Excel-Solver verify your answer to (a).
(6 points)
3. Management of Mr. Taco has completed a study of weekly demand for its “old fashioned tacos” in 23 regional markets. The study revealed the following demand equation:
where Q is the number of tacos sold per store per week and P is the price of its own “old fashioned tacos”. A is the level of local advertising expenditure, pop is the local population and Pc is the average taco price of local competitors. For the typical Mr. Taco outlet, P =$1.50, A = $1000, pop = 40 and Pc = $1.
(a) Estimate the weekly sales for the typical Mr. Taco outlet.
(b) Calculate the price elasticity of demand for Mr. Taco’s “old fashioned tacos”. Also calculate the advertising elasticity and the elasticity of demand with respect to the competitors’ price. Should Mr. Taco raise its taco price? Explain.
(10)
4. In a local hardware store the price of the store brand indoor house paint is $18 per gallon. The daily volume of sales is 30 gallons. The price elasticity of demand for the paint is estimated to be -3. Determine the demand equation for the paint assuming that it is linear.
(8)
5. A soft-drink bottler collected the following monthly data on its sales (measured in thousand units) of 12-ounce cans at different prices.
Month
1
2
3
4
5
6
7
8
9
10
11
12
Price
$0.45
0.50
0.45
0.40
0.35
0.35
0.50
0.55
0.45
0.50
0.40
0.40
Quantity
98
80
95
123
163
168
82
68
96
77
130
125
(a) Using Excel run a linear regression with Quantity the dependent variable and price the independent variable. Provide detailed regression output. Explain if the intercept and the price coefficients are significant. Write the estimated demand equation. Determine by how much the sales volume will increase if price is cut by 10 cents.
(b) Use a log-linear (or log-log) regression to estimate a demand curve of the form
. Provide detailed regression output. Write the estimated demand equation.
Does this regression fit the data better than the linear regression in (a). Determine the price elasticity of demand.
(Hint: The log-linear (or log-log) regression requires you to run a regression of ln Q on ln p, instead of a regression of Q on P. You need to calculate the natural log (or ln) of Q and the natural log of P and run a regression with these natural log data where lnQ is the dependent variable and lnP is the independent variable.)
(24)
