Question 1
Impact of changing price upon revenue and profit
The information about three type of timber is given below:
Fixed production cost =$300
- In order to determine the total cost, it is essential to determine the total variable cost. Hence,
Average variable cost
For pine:
For Myrtle:
Sassafras:
Total cost (TC) would be computed as highlighted below:
Total costs
For pine:
For Myrtle:
Sassafras:
Total revenues
Excel graph for TR and TC
- Point of interaction between the cost and revenue function (using algebra)
For the selected price, TR curve is not intersecting with TC.
Intersection point between TR and TC is at Q=46.15.
Intersection point between TR and TC is at Q=31.58.
- Profit function and break-even point
At break-even point, TR = TC and so, TR and T would intersect.
No breakeven present because TR and TC curves are not intersecting.
Intersection point between TR and TC is which the breakeven quantity is 46.
Intersection point between TR and TC is which the breakeven quantity is 32.
The intersection of total cost (TC) and total revenue (TR) represents the point at which the two values would be equal. Since at this point, the total cost would be equal to the total revenue; hence no profit or loss would be incurred. This is referred to as break-even point. The existence of this point implies that the company can earn profits if the underlying quantity is greater than the break even quantity. Absence of intersection point would imply that breakeven point does not exist which implies that the given product line would be loss making and hence not sustainable.
It is easiest to make profit on Sassafras since the break-even for this insect is achieved at the lowest quantity and hence any quantity greater than the break even quantity of 31.58 would lead to profit generation. Next in line, would be the Myrtle insect for which break even quantity is slightly higher at 46.15 and hence only when 47 insects of this model are sold would the company make profits. However, the company would not make any profit on Pine insect irrespective of the quantity sold.
It is assumed that the fixed costs does not alter and also unit variable cost does not change with the increase or decrease in the units produced. Also, the price charged tends to remain constant.
Question 2
Impact of price discount on revenue
Supply and demand equations are given below:
- Two random numbers for a and b between 0.1 and 0.9 is selected as
- Equilibrium price and quantity would be determined as
Quantity cannot be negative and hence, equilibrium quantity would be 46.5.
- Updated demand equation by considering $15 price decrease.
- New equilibrium price and quantity with the help of algebra is given below:
Quantity cannot be negative and hence, equilibrium quantity would be 51.92.
Equilibrium price
- Demand and supply curve is given below:
- Summary table
|
|
Before price reduction
|
After price reduction
|
Difference
|
|
Equilibrium quantity
|
46.55
|
51.92
|
5.37
|
|
Equilibrium price: consumer pays
|
32.35
|
33.64
|
1.29
|
|
Equilibrium price: restaurant would charge without any price reduction
|
32.35
|
32.35
|
0.00
|
|
Revenue restaurant would receive without any price reduction
|
1505.89
|
1679.6
|
173.72
|
|
Revenue restaurant receives with the price reduction
|
1505.89
|
901
|
704.89
|
Summary
As a result of the price decrease, the demand increase which caused an increase in the equilibrium price and also the equilibrium quantity as the supply remaining the same. However, since there would be a $ 15 cash back, hence even though the total revenue increases but the revenue realised by the restaurant would tend to decrease.
- Based on the given computations, it seems that the price elasticity of demand in the given case is inelastic due to which the percentage increase in quantity is not sufficient to compensate for the decreased revenue realised from every customer. This is clearly reflected in the decreasing revenue that the restaurant has realised on account of the price decrease. Thus, the price decrease by the restaurant is not recommended as it does not increase the overall profits.
- The tacit assumption in the above case analysis is that there would not be any change in the supply function which may be caused due to which non-price factors. Further, it is also assumed that non-price factors do not alter the demand function which continues to remain the same.
