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Basic economic concepts

Problem 1

The R. J. Jones Company is a publisher of cowboy novels - novels about the great western experience, where men were men, horses were horses, and...well, you get the idea. The corporation has hired an economist to determine the demand for its product. After months of hard work and the submission of a REALLY large bill, the analyst tells the company that the demand for the firm's novels (Qx) is given by the following equation:

(Qx) = 12,000 - 5,000Px + 5I + 500Pc

Px is the price charged for the novels, I is income per capita, and Pc is the price of books from competing publishers.
Using this information, the company managers want to:

A. Determine what effect a price increase would have on total revenues.
B. Evaluate how the sale of the novels would change during a period of rising incomes.
C. Assess the probable impact if competing publishers raise their prices.

Assume that the initial values of Px, I, and Pc are $5, $ 10,000, and $ 6, respectively.

Problem 2
Given the following data set, list the point elasticity and the total revenue at each price point. Where is the price elastic, and where is it inelastic? Where is revenue maximized? What is the rational price point? Fully explain.

Price Quantity
$10 1
9 2
8 3
7 4
6 5
5 6
4 7
3 8
2 9
1 10

Problem 3

The following is the production possibilities for a firm. At 0 labor units (strangely enough), there are 0 units produced. At 1 labor unit, there are 10,000 units produced, at 2 labor units, there are 25,000 units produced, at 3 there are 45,000, at 4 there are 60,000, at 5 there are 70,000, at 6 there are 75,000, at 7 there are 78,000, and at 8 there are 80,000. If the price of each unit produced is $ 3, and labor cost is 12,000 per unit, at what level should the firm produce?

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Solution Preview

Please refer attached file for better clarity of tables. Formulas typed with the help of equation writer are missing here.

A. Determine what effect a price increase would have on total revenues.

Determine Qx at Px=$5, I=$10000 and Pc=$6
Lets us find price elasticity of demand at initial level.
Qx=40000 at Px=$5
Price elasticity of demand=Ed=(dQx/dPx)*(Px/Qx)=-5000*(5/40000)=-0.625
So, we find that demand is inelastic at the initial level.
We know that total revenue increases in response to a price increase in case of inelastic demand. So, in the given case total revenue will increase in response to a price increase.

B.  Evaluate how the sale of the novels would change during a period of rising incomes.
We find that coefficient of I is positive in the given equation. We can say that sale of novels
will increase as a result of rising income if other factors remains the same.
In the part (a), we have determined Qx at initial values.
Qx=40000 at Px=$5
Income elasticity of ...

Solution Summary

There are three problems. Solution to first problem explains the effect of rise in income, increase in own prices of novel and its competitors' price on its sales. Solution to second problem finds out revenue maximizing price with the help of price elasticity of demand concepts. Solution to third problem describes the methodology to find optimal output level.