# Maximizing Revenue

Maximizing Revenue

From the scenario, assuming Katrina’s Candies is operating in the monopolistically competitive market structure and faces the following weekly demand and short-run cost functions:

VC = 20Q+0.006665 Q2 with MC=20 + 0.01333Q and FC = \$5,000

P = 50-0.01Q and MR = 50-0.02Q

*Where price is in \$ and Q is in kilograms. All answers should be rounded to the nearest whole number.

Algebraically, determine what price Katrina’s Candies should charge in order for the company to maximize profit in the short run. Determine the quantity that would be produced at this price and the maximum profit possible.

The objective of Katrina’s Candies in this problem is to maximize profit (not revenue). MC (marginal cost) is the change in VC (variable cost) caused by a change in output. In order for Katrina’s Candies to maximize revenue, marginal costs must equal marginal revenue. In order to accomplish their objective, Katrina’s Candies must maximize the difference between total revenue (TR) and total cost (TC) = TR – TC. In order to identify the output level that will maximize profits for the company, the MR and MC functions must be known.

MR = an increase in revenue that results from the sale of one additional unit of output. You calculate marginal revenue by dividing the change in total revenue by the change in output quantity.

MC = the change in total cost that results a change in output. It is derived by dividing the change in total cost by the change in the quantity of the output.

VC = a corporate expense that varies with production output. They vary depending on the company’s production volume. If production increases, variable costs will rise. If production decreases, they will fall. Some examples of variable costs are wages, utilities, materials used in production, etc.

TC = the expenses the company has in supplying its goods and/or services

TR = the amount of total sales of products or services. It is calculated by multiplying the amount of goods and services sold by the price of the goods and services.

FC = they are independent of output. Rent on the building is an example of a fixed cost because regardless of the business’s activity, they are still responsible for paying the rent. There are no fixed costs in the long run because all costs are variable. A great number of costs will be fixed in the short run.

VC = 20Q+0.006665 Q2 with MC=20 + 0.01333Q and FC = \$5,000

P = 50-0.01Q and MR = 50-0.02Q

TC = VC + FC = 20Q+0.006665Q2 + \$5,000

MC = 20 + 0.01333Q

MR = 50 – 0.02Q

MR = MC (where the profit will be maximized)

0.01333Q + 0.02Q = 50 – 20

0.03333Q = 30

50 – 0.02Q = 20 + 0.01333Q

30 = 0.03333Q

Q = 30/0.03333

Q = 900 kgs

P = 50 – 0.01Q

P = 50 – 0.01*900

Revenue (Profit) = TR – TC

P = 50 – 9 = \$41

900*41 – 20*900+5000+0.006665*(810000)

36900 – (23000+5398.65)

=\$8501.35

900 kgs would be the quantity produced at this price and the maximum revenue will be \$8501.

Investopedia. (2016). What is the relationship between marginal revenue and total