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Break-Even Analysis, real GDP, and price elasticity

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1a. A company sells car batteries for $80 each and expects to sell 200,000 units. The variable costs is $28 and fixed costs is $1,000,000. Estimate the break-even point.
1b. If the price is increased to $90, the company expects to lose 10% in sales. Determine the demand curve and the profit function.
1c. Using marginal analysis, determine the price that generates the maximum profits.

2a. Assume the economy consists of the production of only three products: TVs, computers and eateries. Determine the real GDP in 2015 using the data below.
REAL GDP Value Production in Adjacent Years

2104 Quantity Price Expenditure
(in millions) (dollars) (millions of dollars
C TVs 1000 $ 500.00 $ 500,000.00
I Computers 500 $ 500.00 $ 250,000.00
G Eateries 2000 $ 200.00 $ 400,000.00
Y Real and Nominal GDP $ 1,150,000.00

2015 Quantity Price Expenditure
(in millions) (dollars) (millions of dollars
C TVs 1200 $ 350.00 $ 420,000.00
I Computers 600 $ 400.00 $ 240,000.00
G Eateries 2200 $ 175.00 $ 385,000.00
Y Real and Nominal GDP $ 1,045,000.00

3a.
1. Assume the demand function for computers at a retail store has been estimated as follows:
Q = 25,000 - 35(P) + 0.65(I) + 50(CP) + .225(A)
Where Q = quantity of computers demanded, I = Income, C = average price of computers at other stores, and A = advertising expense.
a) If average advertising spending is $40,000, the average price of computers at other stores is $350, and the average income of customers purchasing computers is $60,000, estimate the demand curve for computers at the store?

b) Estimate the price elasticity of demand at the price of $300. Use $325 to determine the change in price.

c) Would you characterize computers as price elastic or price inelastic, based on the above information?

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The questions cover a wide range of economic topics, including Break-Even Analysis, GDP deflator, and price elasticity. The solutions include every step to each the final answers and provide detailed explanation.

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1a. A company sells car batteries for $80 each and expects to sell 200,000 units. The variable costs is $28 and fixed costs is $1,000,000. Estimate the break-even point.

Break-even output = fixed cost/(price - average variable cost) = 1,000,000/(80-28) = 19,231

1b. If the price is increased to $90, the company expects to lose 10% in sales. Determine the demand curve and the profit function.

When price is $90, the sales drops to 200,000 (1-10%) = 180,000
The demand function can be expressed by:
P = a - bQ

We then have the following equation system:
(1) 80 = a - 200,000b
(2) 90 = a - 180,000b
Reorganize (1) and get: a = 80 + 200,000b. substitute this into (2):
90 = (80 + 200,000b)- 180,000b
10 = 20,000b
b = 0.0005
substitute into: a = 80 + 200,000b = 80 + 200,000*0.0005 = 180
Thus, the demand curve is:
P = 180 - 0.0005Q

Profit = （P-AVC）Q - FC
= (180 - 0.0005Q - 28)*Q - 1,000,000
= 152Q - 0.0005Q2 - 1,000,000

1c. Using marginal analysis, determine the price that generates the maximum profits.
The total ...

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