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# ECON 211 Assignment 3

```Qatar University
Department of Finance and Economics
Intermediate Microeconomics
ECON 211
Third Assignment
Pricing and Production
```

Introduction

This assignment seeks to link economic theory with real world. What is required in the first part is to explain the economic theory behind profit maximization for a company operating in perfectly competitive market or in monopolistically competitive market or for a monopolist. The second part requires the use of data and answers to some questions.

Part 1

Explain the theory behind profit maximization with the help of graphs.

Part 2

PoolVac, Inc. manufactures and sells a single product called the “Sting Ray,” which is a patent-protected automatic cleaning device for swimming pools. PoolVac’s Sting Ray accounts for 65 percent of total industry sales of automatic pool cleaners. Its closest competitor, Howard Industries, sells a competing pool cleaner that has captured about 18 percent of the market. Six other vary small firms share the rest of the industry’s sales. Using the last 30 months of production and cost data, PoolVac wishes to estimate its unit variable costs using the following quadratic specification:

The monthly data on average variable cost (AVC), and the quantity of Sting Rays produced and sold each month (Q) are presented in the table below.

PoolVac also wishes to use its sales data for the 26 months to estimate demand for its Sting Ray. Demand for Sting Ray is specified to be a linear function of its price (P), average income for households in the U.S. that have swimming pools (Mavg), and the price of the competing pool cleaner sold by Howard Industries (PH):

The table below presents the last 26 months on the price charged for a Sting Ray (P), average of households with pools (Mavg), and the price Howard Industries charged for its pool cleaner (PH):

 obs Q AVC P MAVG PH 1 1647 109 275 58000 175 2 1664 118 275 58000 175 3 1295 121 300 58000 200 4 1331 102 300 56300 200 5 1413 121 300 56300 200 6 1378 102 300 56300 200 7 1371 105 300 57850 200 8 1312 101 300 57850 200 9 1301 108 325 57850 250 10 854 113 350 57600 250 11 963 114 350 57600 250 12 1238 105 325 57600 225 13 1076 107 325 58250 225 14 1092 104 325 58250 225 15 1222 104 325 58250 225 16 1308 102 325 58985 250 17 1259 116 325 58985 250 18 711 126 375 58985 250 19 1118 116 350 59600 250 20 91 139 475 59600 375 21 137 152 475 59600 375 22 857 116 375 60800 250 23 1003 127 350 60800 250 24 1328 123 320 60800 220 25 1376 104 320 62350 220 26 1219 114 320 62350 220 27 1120 105 315 55000 200 28 1115 110 310 57000 210 29 1137 114 334 58700 235 30 1150 125 350 63000 240

PoolVac, Inc. incurs total fixed costs of \$45,000 per month.

1. Run the appropriate regression to estimate the average variable cost function (AVC) for Sting Rays. Copy and paste the results from Excel and write down the estimated AVC.
1. Evaluate the statistical significance of the three estimated parameters using a significance level of 5 percent.
1. Comment on the algebraic signs of the three parameter estimates.
1. Write the estimated total variable cost, average variable cost, and marginal cost functions (TVC, AVC, and MC) for PoolVac.
1. Find the quantity where average variable cost is minimized and compute the minimum average variable cost.
1. Run the appropriate regression to estimate the demand function for Sting Rays. Copy and paste the results from Excel and write down the estimated demand function.
1. Evaluate the statistical significance of the three estimated slope parameters using a significance level of 10 percent.
1. Discuss the appropriateness of the algebraic signs of each of the three slope parameter estimates.
1. The manager at PoolVac, Inc. believes Howard Industries is going to price its automatic pool cleaner at \$250, and average household income in the S. is expected to be \$65,000. Using the regression results from part 2 a, write the estimated demand function, inverse demand function (P as a function of Q), and marginal revenue function.
1. Using your estimated cost and demand function from part 1 and 2, what price would you recommend the manager of PoolVac, Inc. charge for its Sting Ray? Given your recommended price, estimate the number of units PoolVac can expect to sell.
1. Given your recommended price, estimate the monthly total revenue, total cost, and profit of PoolVac.
1. For the profit maximizing solution in question 3, compute the point elasticity of demand for Sting Rays.

In the profit maximizing situation in question 3, a 5 percent price cut would be predicted to _______________ (increase, decrease) quantity demanded of Sting Ray by _________ percent, which would cause total revenue to _____________ (rise, fall, stay the same) and profit to _____________ (rise, fall, stay the same).

1. a. For the profit maximizing solution in question 3, compute the income elasticity of demand for Sting Rays.
1. Is the algebraic sign of the income elasticity as you expected? Explain.
1. A 10 percent increase in Mavg would be predicted to ___________ (increase, decrease) quantity demanded of Sting Rays by __________ percent.
1. a. For the profit maximizing solution in question 3, compute the cross-price elasticity of demand for Sting Rays.
1. Is the algebraic sign of the income elasticity as you expected? Explain.
1. A 3 percent decrease in PH would be predicted to ____ (increase, decrease) quantity demanded of Sting Rays by _________ percent.
1. If total fixed cost increase from \$45,000 to \$55,000, what price would you now recommend in order to maximize profits at PoolVac? Compute the number of units sold at this price, total revenue, total cost and profit.
1. If the manager of PoolVac wanted to maximize total revenue instead of profit (a bad idea), the manager would charge a price of ________. At this price, PoolVac’s profit would be ________, which is __________ (higher than, lower than, the same as) the profit in question 3.