Answer to Question #340506 in Macroeconomics for Shey

Question

Assume that ABC Company has fixed production costs of $70 per unit, and marginal cost of production is $0.4 per unit. ABC sells for $0.5 per unit. a) Write down the associated cost, revenue, and profit functions. b) What profit (or loss) results from the sale of 500 units of products? c) How many units of output should be produced and sold in order to break even?

Answer 1

Solution

a)Since the fixed cost for company ABC is $70 and the marginal cost is $0.4 per unit, the cost function will be:

y = 70 + 0.4 * x

where x is the number of products produced

The income function will look like this at a selling price of $0.5 per unit:

y = 0.5 * x

where x is the number of products sold

If we subtract the cost function from the income function, then we get the profit function, which will have the following form:

у = (0,5*х) - (70+0,4*х) = 0,5*х - 0,4*х -70 = 0,1*х -70

where x is the number of products sold

b) The profit function for selling 500 units would be:

у = 0,1 * 500 - 70 = 50 -70 = -20

When selling 500 units of a product, ABC has a loss of $20. This means that 500 units of products are not enough to cover fixed costs of $70

c)At the break-even point, ABC will have neither profit nor loss, and the profit function will be as follows:

у = 0,1*х - 70 = 0

Then the number of products sold to reach the break-even point will be equal to:

х = 70/0,1 = 700

To cover the fixed costs of $70, it is necessary to produce and sell 700 units of products.

Answer: а)y = 70 + 0.4 * x;

y = 0.5 * x;

у = 0,1*х -70.

b) When selling 500 units of products, a loss of $20 is formed.

c)It is necessary to produce and sell 700 units of products to reach the break-even point.