Auto Maintenance Services (AMS) is a small auto service outlet in a suburban area of Syracuse. In reaction to a small increase in wages that has caused the marginal cost of this auto service establishment to increase from $25 to $30, the owner is considering raising the prices of the services AMS offers. The owner's daughter, who is studying economics and takes care of her father's books and finances advises him against that. She has estimated that if AMS raises its prices it will face the weekly demand curve Q = 140 - 2.5 P, whereas if it lowers its price it will face the demand curve Q'= 55-.625P.
a. Determine the (average) price AMS is charging for its services, presently.
b. Determine the number of cars it services each week.
c. Using the point price elasticity formula, calculate the elasticity measures of the demand AMS faces at its present (average) price.
d. Assuming that the owner's daughter is correct, what is the MC range within which AMS should not change its price?
e. AMS's weekly total fixed cost is $250. Assuming that the firm's marginal cost and average variable cost are equal (AVC =MC), determine its weekly profit after the wage increase.
f. What should AMS do if its MC goes up to $40? Explain.
a. To determine the average price AMS is currently charging for its services, we need to find the equation where demand equals the quantity supplied. In other words, we need to equate the two demand curves.
Q = Q'
140 - 2.5P = 55 - 0.625P
Simplifying the equation, we get:
85 = 1.875P
P = 85 / 1.875
P ≈ $45.33
Therefore, the average price AMS is currently charging for its services is approximately $45.33.
b. To find the number of cars AMS services each week, we can substitute the average price (P) into either of the demand curves and solve for Q.
Using the first demand curve:
Q = 140 - 2.5P
Q = 140 - 2.5 * 45.33
Q ≈ 140 - 113.33
Q ≈ 26.67
Therefore, AMS services approximately 27 cars each week.
c. The formula for price elasticity of demand (ε) is given by:
ε = (% change in quantity demanded) / (% change in price)
To calculate the elasticity at the current price, we can use the midpoint formula:
ε = (Q2 - Q1) / (Q2 + Q1) / (P2 - P1) / (P2 + P1)
Substituting the values into the formula:
ε = (27 - 26.67) / (27 + 26.67) / (45.33 - 30) / (45.33 + 30)
ε ≈ 0.33 / 53.67 / 15.33 / 75.33
ε ≈ 1.35
Therefore, the elasticity of demand AMS faces at its current price is approximately 1.35.
d. The owner's daughter advises against changing the price when the marginal cost (MC) is within a certain range. To find that range, we need to compare the marginal cost with the price elasticity of demand.
If ε < 1, it indicates that demand is inelastic and a change in price will have a relatively smaller impact on quantity demanded. In this case, the price should not be changed.
If ε > 1, it indicates that demand is elastic and a change in price will have a relatively larger impact on quantity demanded. In this case, the price should be changed cautiously.
Since the elasticity at the current price is 1.35, it falls in the elastic range. Therefore, the MC should not change the price if it is within a range that keeps the demand elastic. The specific MC range would depend on the exact price elasticity values and business considerations.
e. To determine the weekly profit after the wage increase, we need to calculate the average variable cost (AVC).
AVC = MC = $30 (given)
Total variable cost (TVC) = AVC * Q = $30 * 27 = $810
Total cost (TC) = TVC + Total fixed cost (TFC) = $810 + $250 = $1060
Revenue (R) = P * Q = $45.33 * 27 = $1224.91
Profit (π) = R - TC = $1224.91 - $1060 = $164.91
Therefore, AMS's weekly profit after the wage increase is approximately $164.91.
f. If AMS's MC goes up to $40, the owner should consider adjusting the prices due to the change in cost. However, the decision should be made based on the elasticity of demand.
The owner's daughter has estimated the demand curve when the price is lowered to be: Q' = 55 - 0.625P
To determine the new equilibrium point, we set MC equal to the new demand equation:
MC = 40 = 55 - 0.625P
Solving for P, we get:
0.625P = 55 - 40
0.625P = 15
P = 15 / 0.625
P ≈ $24
Therefore, if the MC increases to $40, AMS should consider lowering its price to approximately $24 to maintain demand and profitability.