Question

A firms demand function for a good is given by P = 107-2Q and
their total cost function is given by TC = 200+3Q. (using for 6.1
to 6.4)

6.1 Obtain an expression for total revenue (price X quantity)
in terms of Q

6.2 For what values of Q does the firm breakeven?

6.3 Illustrate the answer to (ii) using sketches of the total
cost function, the total revenue function and the profit
function

6.4 From the graph estimate the maximum profit and the level
of output for which profit is maximized

Answer #1

Your hospital has a demand function given by P = 404 - 2Q where
P is the price of hospital care and Q is the quantity of hospital
care. The marginal revenue (MR) function is given by MR = 404 – 4Q.
The total cost function (TC) is given by TC = 300 + 4Q +
8Q2 and the marginal cost (MC) is given by MC = 4 +
16Q.
Find the total revenue (TR) function which is a function...

Consider a firm with the demand function P(Q)=(50-2Q), and the
total cost function TC(Q)=10,000+10Q. Find the profit maximizing
quantity. Calculate the profit maximizing price (or the market
price). Hint: MR(Q)=(50-4Q),

The market demand function for a good is given by Q = D(p) = 800
− 50p. For each firm that produces the good the total cost function
is TC(Q) = 4Q+ Q^2/2 . Recall that this means that the marginal
cost is MC(Q) = 4 + Q. Assume that firms are price takers.
(a) What is the efficient scale of production and the minimum of
average cost for each firm? Hint: Graph the average cost curve
first.
(b) What...

Price Discrimination
Suppose the demand for ticket sales is given by the following
function: P =315−2Q
Further suppose that marginal cost is 3Q and total cost is
3/2Q^2
a) Find the profit maximizing price and quantity. 1
b) What is the maximum profit?
Suppose now that the ticket seller can price discriminate by
checking IDs. There are two
demands in the market:
Adult Demand: PA = 315 − 3Q
Student Demand: PK = 315 − 6Q
Again, suppose that marginal...

Suppose the market demand for a good is given by P = 60 – 2Q.
Also, there is an incumbent firm already in the market, and a
potential entrant. Let’s call the incumbent firm Firm 1, and the
potential entrant Firm 2. Each firm has an identical Total Cost of
production given by TC = 128 +4q, where q is the quantity of output
produced by that firm. MC for each firm = 4.
a) What is Firm 2’s Best...

if the marginal cost of a firm is MC = 9q^2 + 2q +1 and the
marginal revenue MR = 60-q. Given that total cost is 3390 when q
-10
(a) Derive an expression for total cost
(b) Derive the expression for total revenue
(c) Using the results from (a) and (b) find the total profit
function

The market demand curve is P = 90 − 2Q, and each firm’s total
cost function is
C = 100 + 2q2.
Suppose there is only one firm in the market. Find the
market
price, quantity, and the firm’s profit.
Show the equilibrium on a diagram, depicting the demand function
D (with the vertical and horizontal intercepts), the marginal
revenue function MR, and the marginal cost function MC. On the same
diagram, mark the optimal price P, the quantity Q,...

Example 1:
Suppose a monopolist faces an inverse demand function as p = 94
– 2q. The firm’s total cost function is 1.5q2 + 45q +
100. The firm’s marginal revenue and cost functions are MR(q) = 90
– 4q and MC(q) = 3q + 45.
How many widgets must the firm sell so as to maximize its
profits?
At what price should the firm sell so as to maximize its
profits?
What will be the firm’s total profits?

Consider a market in which the demand function is
P=50-2Q,
where Q is total demand and P is the price. In the market, there
are two firms whose cost function is
TCi=10qi+qi^2+25,
where qi1 is the quantity produced by firm i and
Q=q1+q2
Compute the marginal cost and the average cost.
Compute the equilibrium (quantities, price, and profits)
assuming that the firms choose simultaneously the output.

3. Suppose a monopolistically competitive firm’s demand is given
by P = 4,000 – 2Q And its cost function is given by TC = 5 + 40Q a.
Find the profit maximizing quantity, price, and total profit level.
b. If the firm is regulated to charge Price = Marginal Cost,
calculate how much profit it will make.

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