1. An auto-service establishment has estimated its monthly cost function as follows:

TC = 6400 + 8 Q
Where Q is the number of cars it services each months and TC represents its total cost.
The firm is targeting $3,200 net monthly profit with an output target of servicing 3000 cars per month.
a. Determine the firm’s markup ratio and the price it would have to charge to make its targeted profit.
b. Now suppose the demand curve the firm faces is:
Q = 2760 – 50 P
Is the firm going to achieve its target profit? Explain.
c. If your answer to (b) is “no”, what price would you recommend that the firm charge? Explain.

a) Use algebra. expected TC=6400+8*3000 = 30400. Adding on targeted monthly profit, total revenue must be 30400+3200 = 33600. Ergo, price must be 33600/3000= 11.2

b) clearly no. even if it charged zero, it couldn't service 3000 cars. Plug in 11.2 into P, then calculate profit/loss.

c) always always, where marginal cost = marginal revenue. (Assume, for now, there are no long term consequences or moral issues from screwing the customer.) MC from your first statement is 8. Now to determine marginal revenue. 1st, using algebra, rewrite the demand equation to be in terms of P.
I get P=55.2-.02*Q.
Now then total revenue is P*Q = 55.2*Q + .02*Q^2. Take the first derivitive and marginal revenue becomes 55.2-.04*Q. Set this equal to 8 (MC) and solve for Q. Plug the value for Q into the rewritten demand equation to solve for P. (hint, for P I get $31.60)

Lotsa luck.

I understand how you got the price and all but i don't get how you find the markup ratio or is that 11.2? Thanks for your help

Another question, for part C...would you put the new Q(1180) into the profit equation to get the suggested price. Say, 3200(target profit)=1180P-15840(6400+8*1180), which then the price would be 16.14??

Mark-up ratio, as I understand, is the difference between the selling price and the buying price, divided (usually) by the selling price. I believe, in your case, the markeup ratio would be (11.2-8.0)/11.2 = 28.6%

(While I understand the economics of your question, the nomenclature of accounts and managers has frequently escaped me.)

No. I would put Q(1180) into the demand equation P=55.2 - .02Q Here P=31.6. Thus, total revenue would be 31.6*1180 = 37288. Total costs are 6400 + 8*(1180) = 15840. Monthly profits become $21448.

But, as I hinted in my "nomenclature" note in my last post, economists do not think of problems in terms of "targeted profits" We always try to find the "maximum profits" solution. To me, "targeted profits" is a completely foreign concept.

Thank you for your help with this problem...i understand things alot better now.....the only other thing is my prior post i asked about the markup ratio? Is it the same as the price?

In a prior post .. Markup ratio is (price - cost)/price

I need help with understanding this problem scenario.Generalized Demand function Qd =1,800-20P+0.6M-50Pr. So
question A is looking at the function D2 income is $19,500 and the price of related good is 250. Next, it wants you to sketch begining with D2 if there is a decrease in income causing comsumers to be willing and able to purchase 300 fewer units at each price. Find the new deman curve and label it D3, What is the equation fo D3, By how much must income fall to cause the shift from D2 to D3? Help

Explain Bot Explain Bot answered
8 months ago

To solve this problem, let's break it down step by step:

a) The demand function is given as:
Qd = 1,800 - 20P + 0.6M - 50Pr

In this scenario, income (M) is $19,500 and the price of the related good (Pr) is $250. To find the initial demand curve D2, we need to substitute these values into the demand function.

Qd2 = 1,800 - 20P + 0.6(19,500) - 50(250)
Qd2 = 1,800 - 20P + 11,700 - 12,500
Qd2 = -9,000 - 20P

Now, let's move on to the next part of the question.

b) If there is a decrease in income causing consumers to be willing and able to purchase 300 fewer units at each price, we need to find the new demand curve D3.

To find the equation for D3, we subtract 300 from the previous demand curve, Qd2.

Qd3 = -9,000 - 20P - 300
Qd3 = -9,300 - 20P

Now, let's analyze the last part of the question.

c) We need to determine by how much income must fall to cause the shift from D2 to D3.

To find the change in income, we need to compare the coefficients of M in the demand equations.

Coefficient of M in D2 = 0.6
Coefficient of M in D3 = 0 (as it's not present in the equation)

Therefore, income must fall by 0.6 * 19,500 = $11,700 for the shift from D2 to D3.

To summarize:
a) D2 equation: Qd2 = -9,000 - 20P
b) D3 equation: Qd3 = -9,300 - 20P
c) Income must fall by $11,700 for the shift from D2 to D3.

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