Question

P1 A marketing analyst has estimated a firm’s demand function to be ?? = 40 ? 2?? + 20??, where X is an indicator for whether the economy is in a boom (X = 1) or recession (X = 0). Marginal cost of producing the good is 10.

i) Write down the inverse demand, i.e. P as a function of Q and X.

ii) Write down the marginal revenue function during a boom as a function of Q.

iii) What is the firm’s optimal price during a boom?

iv) Write down the marginal revenue function during a recession as a function of Q.

v) What is the firm’s optimal price during a recession?

P2 A snack company’s data analysts have estimated the following elasticities for sales of the firm’s products. Price elasticity is –2.5. Income elasticity is –0.8. Cross-price elasticity with chocolate bars is +0.5. Advertising elasticity is +0.8. Marginal cost is $6.

i) What is the optimal profit margin (P – MC)/P in percent?

ii) What is the optimal price?

iii) If the price of chocolate bars increases by 10%, by how much do the sales of the company change? (Pay attention to the right sign.)

iv) If the price of chocolate bars increases by 10%, and consumer incomes decrease by 5% at the same time, by how much do the sales of the company change? (Pay attention to the right sign.)

v) If the firm wants to achieve 20% sales growth, by how much does it need to increase its advertising expenditure?

P3 Consider the cost function ?? = 40 + 3?? ? 2?? ? + ? ? ?? ? .

i) At Q = 4, what is the firm’s average fixed cost?

ii) At Q = 4, what is the firm’s marginal cost?

iii) If the firm optimally produces Q = 4, and ?? = 35 ? ????, what does a have to be?

iv) Which Q minimizes the firm’s average variable cost?

v) What is the firm’s minimum average variable cost?

P4 A firm makes two goods, A and B, with production functions ?? ? = 2?? ?(?? ?) ? and ?? ? = 16?? ?+4?? ? . The firm has a fixed total supply of capital of 1 unit, and it can hire labor at PL = $10 for the first 5 hours, and for the overtime rate of PL = $20 after that, up to 10 hours. Output prices are P A = $2 and P B = $1.

i) So that capital’s marginal revenue product is equal for A and B, what must L A be?

ii) How much labor should the firm hire to work on B?

iii) If K A = 1, what is the overall revenue from QA and QB?

iv) If K A = 0, what is the overall revenue from QA and QB?

v) What is the profit contribution (revenue minus labor cost)?

Answer #1

A marketing analyst has estimated a firm’s demand function to be
?? = 40 ? 2?? + 20??, where X is an indicator for whether the
economy is in a boom (X = 1) or recession (X = 0). Marginal cost of
producing the good is 10. i) Write down the inverse demand, i.e. P
as a function of Q and X. ii) Write down the marginal revenue
function during a boom as a function of Q. iii) What is...

Q1. A monopolist has the following
demand function and marginal cost function P = 120 – Q and MC = 30
+ Q.
i. Derive the monopolist’s marginal revenue function.
ii. Calculate the output the monopolist should produce to
maximize its profit.
ii. (continuation)
iii. What price does the monopolist charge to maximize its
profit?
Now assume that the monopolist above split into two large firms
(Firm A and Firm B) with the same marginal cost as the
monopolist.
Let...

Please show all steps to the 5 solutions:
A firm makes two goods, A and B, with production functions ??^A
= 2??^A(??^A)^2 and
??^B = 16??^B+4??^B. The firm has a fixed total supply of capital
of 1 unit, and it can hire labor at PL = $10 for the first 5 hours,
and for the overtime rate of PL = $20 after that, up to 10 hours.
Output prices are PA = $2 and PB = $1.
i) So that...

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,...

Consider the cost function C= 40 + 3Q 2Q^2 + 1/2Q^3 . i) At Q =
4, what is the firm’s average fixed cost? ii) At Q = 4, what is the
firm’s marginal cost? iii) If the firm optimally produces Q = 4,
and P = 35-aQ, what does a have to be? iv) Which Q minimizes the
firm’s average variable cost? v) What is the firm’s minimum average
variable cost?99

a) Assume the firm operates in the monopoly market in the long
run with the demand function P = 100-Q and TC = 640 + 20Q with TC
showing the total cost of production, Q and P respectively of
output quantity and price. Using the information above,
publish
i) Total revenue function (TR)
ii) Marginal revenue (MR)
iii) Marginal cost function (MC)
iv) Determine the level of price and quantity of production that
maximizes profit
v) Determine the amount of...

The market demand is given by P = 90 − 2Q. There are only two
firms producing this good. Hence the quantity supplied in the
market is the sum of each firm’s quantity supplied (that is, Q = qA
+ qB), where qj is the firm j 0 s quantity supplied). Firm A has
zero marginal cost, while Firm B has the marginal cost of $30. Each
firm has no fixed cost, and simultaneously chooses how many units
to produce....

Monopolistically competitive firm with
a demand of Q = 630 – 3P
a total cost function of C(Q) = 25,000 + 10Q.
1. What is the profit-maximizing output level
2. What is the profit or loss from producing at the optimal
level and charging the optimal price
3. At the optimal price and quantity combination, what is your
firm's marginal revenue
4. If your firm's advertising elasticity is 0.02, what is the
optimal amount for you to advertise

A monopolist practices third degree price discrimination by
separating its customers into two groups: consumers under 65 and
senior citizens. Themonopolist’s marginal cost is MC = 0.05q, where
q is the total output in both markets. The marginal cost
does not depend on the market in which the goods are sold.The
demand curves are
! Adults: PA = 25 – 1/6 × QA = 25 –
0.1667 × QA
! Seniors: PS
= 15 – c × QS = 15 – 0.125 ×...

consider market with demand function q = 200 - 2p. In this
market there is a dominant firm and a competitive fringe of small
firms. The competitive fringe takes the price of the dominant firm
as given and offer an aggregate output S = p - 70; (p > 70),
where p is the price quoted by the dominant firm. The residual
demand is covered by the dominant firm. Determine the optimal
solution for the dominant firm assuming that its...

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