The demand of a certain product is linearly dependent on its price. That price-d

Question

The demand of a certain product is linearly dependent on its price. That price-demand function is given by: x=x(p)=200?0.5 p The cost function is given by: C(x)=3000+15x A) What is the demand when the price is $20? What is the demand when the price is $100? B) Give the revenue function R(x) for this product. What is the domain for the revenue function? C) Sketch the Revenue and Cost function on the same graph over the domain given in part B. D) Identify the break-even points for this product. E) For what demand is the product generating a profit? F) For what demand is the product generating a loss? G) For what price is the product generating a profit or a loss?

Explanation / Answer

A demand function gives the number of items consumers are willing to buy at a given price, and a higher price generally results in a lower demand. However, as the price rises, suppliers will be more inclined to produce these items (as opposed to spending their time and money on other products), so supply will generally rise. A supply function gives q, the number of items suppliers are willing to make available for sale, as a function of p, the price per item.

Linear Supply Function, Equilibrium Price

A supply equation or supply function expresses q (the number of items suppliers are willing to make available) as a function of the unit price p (the price per item). A linear demand function has the form

Interpretation of m
The (usually positive) slope m measures the change in supply per unit change in price. Thus for instance, if p is measured in dollars and q in monthly sales, and m = 400, then each $1 increase in the price per item will result in an increased supply of 400 items per month.

Interpretation of b
The y-intercept b gives the number of items suppliers would be willing to supply for free.

Example
The number of T-shirts I am prepared to tie-dye and supply to Campus Creations Inc. per day depends on the price, $p, I obtain according to

For every $2 increase in price, I am willing to supply 5 additional shirts per day.

Equilibrium Price
Demand and Supply are said to be in equilibrium when demand equals supply. The corresponding values of p and q are called the equilibrium price and equilibrium demand. To obtain the equilibrium price, set demand equal to supply and solve for the unit price p. To obtain the equilibrium demand, evaluate the demand (or supply) function at the equilibrium price.

http://answers.mheducation.com/economics/economics/demand-supply-and-market-equilibrium

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