Answer to Question #150118 in Microeconomics for Nwajei Simon

Question

In the aftermath of a hurricane, an entrepreneur took a one-month leave of absence (with out pay) from her $5,000-per-month job in order to operate a kiosk that sold fresh drinking water.During the month she operated this venture, the entrepreneur paid the government $2,500 in kiosk rent and purchased water from a local whole sale rata price of $1.34 per gallon.Write an equation that summarizes the cost function for her opera- tion, as well as equations that summarize the marginal, average variable, average fixed, and average total costs of selling fresh drinking water at the kiosk. If consumers were willing to pay $2.25 to purchase each gallon of fresh drinking water, how many units did she have to sell in order to turn a profit? Explain carefully.

Answer 1

The entrepreneur’s new venture has two kinds of costs, one is fixed in nature and the other varies. Since the entrepreneur is leaving her job that pays her $5,000 per month, this becomes her opportunity cost. Along with this, she is paying $2,500 to the government as rent. Hence the total fixed cost becomes $7,500.

The purchasing power of 1 gallon water from local wholesaler is $1.34. The entrepreneur does not know how many gallons will yield her a profit. Hence the key variable that varies in this case is the quantity of water in gallons Q.

The cost function becomes:

$C(Q) = 7500 +1.35Q$

Marginal Cost: It is the first derivative of the total cost with respect to the output:

$MC(Q) = \frac{∂TC}{∂Q} \\ = \frac{∂(7500+1.34Q)}{∂Q} = 1.34$

Hence the marginal cost is $1.34 per gallon.

Average fixed cost: It is defined as fixed cost per unit of output produced:

$AFC(Q) = \frac{FC(Q)}{Q} = \frac{7500}{Q}$

Hence the equation that describes the average fixed cost is $\frac{7500}{Q}$

Variable cost varies with the level of output. It is the difference between total cost and fixed cost for each level of output.

For 100 units of output, variable cost is $15,000 ($30,000 - $15,000).

Thus, for 100 units of output produced, average variable cost is $100.

Average total cost: It is the total cost divided by the number of units produced:

$ATC(Q) = \frac{TC(Q)}{Q} \\ = \frac{7500+1.34Q}{Q} \\ = \frac{7500}{Q} + 1.34$

Hence the average total cost acquires the equation, $ATC(Q) = \frac{7500}{Q} + 1.34$

As far as her revenues are concerned, consumers pay $2.25 per gallon of water purchased. Thus the total revenue function is TR(Q) = 2.25Q

In order to start earning profit, the entrepreneur should sell the quantity of water that would at least earn her the total cost incurred, that is, her cost is covered. To compute this level, equilibrates Total cost and Total revenue functions:

$C(Q)=TR(Q) \\ 7500 +1.34Q = 2.25Q \\ 7500 = 0.91Q \\ Q = 8242$

Hence, the entrepreneur must sell at least 8242 gallons of water to start earning profit.