Northern Caribbean University
Department of Professional and Continuing Education
ECON 170: Business and Economic Calculus
Assignment (15%)
Due Date: April 29, 2021
Facilitator: Du-Warner Mckenzie
ID #: Sherian Wedderburn 20181600, Tashique Strickland 31061498, Shay Robinson
20142392 Score:_______
Instruction: Answer ALL questions. Full marks will only be awarded to answers that are
thoroughly solved.
1. Define the following terms, using appropriate examples where necessary. Each values
four (4) marks
a) Price Demand Function- is a mathematical equation which expresses the demand of a
product or service as a function of its price and other factors such as the prices of the
substitutes and complementary goods and income. The demand function has the form y =
mx + b, where “y” is the price, “m” is the slope and “x” is the quantity sold.
b) Cost Function – A cost function is a mathematical formula used to chart how production
expenses will change at different output levels. In other words, it estimates the total cost
of production given a specific quantity produced. The cost function equation is expressed
as C(x)= FC + V(x), where C equals total production cost, FC is total fixed costs, V is
variable cost and x is the number of units.
c) Revenue Function- A formula or equation representing the way in which particular items
of income behave when plotted on a graph For example, the most common revenue
function is that for total revenue in the equation y=bx, where y is the total revenue, b is
the selling price per unit of sales, and x is the number of units sold.
d) Profit Function- Profit function is a mathematical relationship between a firm’s total
profit and output. It equals total revenue minus total costs, and it is maximum when the
firm’s marginal revenue equals its marginal cost. Our profit function equation will be as
follows: P(x) = R(x) – C(x).
e) Breakeven Point- This is a critical number that must be analyzed within a business. It’s
the point where sales and expenses are the same or when the sales of a compny are
enough to cover the expenses of the business. The break-even point formula in units is
Fixed Costs / (Sales Price Per Unit – Variable Costs Per Unit). For example: Say you
own a toy store and want to find your break-even point in units. Your fixed costs total is
$6,000, your variable costs per unit is $25, and your sales price per unit is $50. Plug your
totals into the break-even formula to find out your break-even point in units.
$6,000 / ($50 – $25) = 240 units. You need to sell 240 units to break even
2. An object moves along the y axis (marked in feet) so that its position at time x (in seconds) is
2x3 -8x2 + 7x
