TFC = $1,000
MC = $1 (and constant)
2.Assume that all households have the same demand schedule which is given by the following relationship: P = 10 – 2Q. If there are 400 households in the market, state what the market demand schedule and marginal revenue schedule look like facing the monopolist.
3.Using the information in the item above, find the monopolist’s profit-maximizing output and price
4.Suppose the monopolist is to behave as though it is in a perfectly competitive market. What price would the monopolist charge and how many units of output work it produce? Does the monopolist earn a profit or loss and how much is it?
2) MR = a + 2bQ.
3) Set MR = MC or 10 - 2Q = 1. Solve for Q. This is the profit-maximizing quantity. Sub the answer you get for Q into the demand function to determine the profit-maximizing price.
4) In a perfectly competitive firm, MR = P. Follow steps in #3, but use 10 - 2Q = 1 for MR = MC. Last, use the cost function C = 1000 + 1Q to determine profit or loss.
2) Market demand function is:
P=10 - (2/400)Q = 10-.005Q
3) You could solve 3 in two ways; directly by determining the Marginal Revenue from the Market demand in 2) above, or as Dwane does by maximizing over a single household then multiplying by 400.
BTW, Dwane's MR in #3 is not correct. MR=10-4Q.
4) Dwane is correct
It sure is incorrect...wow! The bad thing is that I wrote the correct formula directly above! It always good to have someone double-check your work!
3) MR= 10-4Q=1
Q=2.25
P=10-.1(2.25)
P=$9.775
Is this what you mean?
OR should you times the answers you get for Q and P by 400?
To find the market demand schedule and marginal revenue schedule facing the monopolist, we need to use the given demand schedule for all households, which is P = 10 - 2Q, where P is the price and Q is the quantity.
Market demand schedule: To get the market demand schedule, we need to sum up the individual demand of all households. Since all households have the same demand schedule, we can multiply the demand equation by the number of households (400) to obtain the market demand schedule:
P = 10 - 2Q
Market demand schedule: P = 10 - 2(400)Q
Simplifying, we get: P = 10 - 800Q
Marginal revenue schedule: The marginal revenue schedule represents the change in total revenue resulting from a one-unit change in quantity. To find this, we need to derive the marginal revenue function from the market demand schedule. The formula for marginal revenue (MR) is MR = a + 2bQ.
Comparing this formula with the market demand schedule, we can see that a = 10 and 2b = -800. Solving for b, we find b = -400. Substituting the values of a and b into the formula, we get:
MR = 10 + (-400)Q
Simplifying, we get: MR = 10 - 400Q
Now, to find the monopolist's profit-maximizing output and price, we need to set the marginal revenue (MR) equal to the marginal cost (MC). The given marginal cost is $1, so we can equate MR and MC to find the profit-maximizing quantity.
MR = MC
10 - 400Q = 1
Solving for Q, we get: Q = (10 - 1) / 400 = 0.0225
Substituting the value of Q into the demand function, we can find the profit-maximizing price:
P = 10 - 2Q = 10 - 2(0.0225) = 10 - 0.045 = 9.955
Therefore, the monopolist's profit-maximizing output is approximately 0.0225 units and the price is approximately $9.955.
Now, let's consider how the monopolist would behave as though it is in a perfectly competitive market. In a perfectly competitive market, the monopolist takes the market price as given and produces where marginal cost equals market price.
MR = P
10 - 400Q = P
Set MR equal to MC:
10 - 400Q = 1
Solving for Q, we find:
Q = (10 - 1) / 400 = 0.0225
Substituting the value of Q into the demand function, we can find the price:
P = 10 - 2Q = 10 - 2(0.0225) = 10 - 0.045 = 9.955
Therefore, in a perfectly competitive market, the monopolist would charge a price of approximately $9.955 and produce approximately 0.0225 units of output.
To determine whether the monopolist earns a profit or loss, we need to calculate the total cost (TC) and compare it to the total revenue (TR) generated from selling the units of output Q.
The cost function is given as C = 1000 + 1Q. Substituting the value of Q, we get:
C = 1000 + 1(0.0225) = 1000 + 0.0225 = 1000.0225
Total cost (TC) = C * Q = 1000.0225 * 0.0225
Total revenue (TR) = P * Q = 9.955 * 0.0225
To determine profit or loss, we calculate the difference between total revenue and total cost:
Profit/Loss = TR - TC
Evaluate the above expression using the calculated values for TR and TC to determine the exact amount of profit or loss.