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Suppose a firm with market power faces the following inverse demand P=4-(Q/20) The firm has the cost function C= 100 +8.4Q-(5/4)Q^2+(1/30)Q^3. 

a.Calculate the firm's market power as measured by the Lerner Index.

b. Suppose the firm is contemplating investing $5 in R&D that, if successful, would change the demand to P=6-(Q/20) and the cost function to C=50+8.5Q-(7/10)Q^2+(1/60)Q^3. Find the minimum probability of success needed to convince the firm to invest in innovation. 

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Kristelle Balando
Kristelle BalandoLv10
29 Sep 2019

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Related questions

1. Consider a single firm facing inverse demand function
p=100-10q
where q is the quantity of the good produced and p is the price for the good.
The firm has a linear cost function C(q)=10q.
Find the firm's profit-maximizing quantity, q*.

2. Suppose now two firms are facing inverse demand function
p = 100 - 10Q
where Q=q_1 + q _ 2 is the total quantity of the good produced and p is the price for the good.
Each firm has linear cost function C(q) = 10q .
Find the competitive equilibrium output, Q *

3. Compare the monopoly price in Q1, call it p^M, to the competitive equilibrium price in Q2, call it p^CE,
What is p^M - p^CE

4. Consider the alcohol consumption problem (e.g., Tadelis 1.4) and suppose your payoff is given by
v (a ; theta)= (theta*a) - c*a^2
where c > 0 is the cost of consuming amount a and theta belongs to [1,6] is your tolerance for alcohol.
Find your optimal consumption when theta is distributed uniformly on the interval [1,6].

1. You are given costs for a firm in the following table.

Quantity Total Cost Variable Cost Fixed Cost Marginal Cost
10 35.7 ? $10 ?
11 ? 47.8 ? ?
12 ? ? ? 32

From the information given, calculate the Average Variable Cost when the firm produces 12 units. Round your answer to one decimal.

2.

Demand is given by:

Q = 2000 - 223P + 8P' + 180Y, and P = 8, P' = 9, and Y = 4

Calculate the Income Elasticity of Demand at Y = 4? Round your answer to two decimal places.

3.

Suppose the cost function is C(Q) = 49 + 5Q + 6Q2 + 8Q3. What is the average fixed cost of producing 79 units?
Please round answer to one decimal place.


4.

A firm faces the following demand:

Q = 109 - 0.21P

The firm's cost function is:

C = 5Q2 + 99Q + 1,896

How much profit does this firm earn when it produces the quantity, Q, that maximizes profit?

1. All of the following are characteristics of long-run equilibrium for firms in a monopolistically competitive market except:

A. price equals marginal cost.

B. price equals average total cost.

C. price exceeds the minimum of the average total cost.

D. marginal cost equals marginal revenue.

2. All of the following are strategies a firm with market power can adopt to increase its profits over time except:

A. erecting barriers to entry.

B. setting price equal to the marginal costs of production.

C. mergers with, and acquisitions of, competing firms.

D. influencing the regulatory process.

3. Assume that for a particular firm's output price = $80, marginal cost = $30, average total cost = $25. Based on this information, the firm's Lerner Index is equal to:

A. 0.313.

B. 0.625.

C. 0.6.

D. 0.375.

4. Assume that when the price is $20, the quantity demanded is 9 units, and when the price is $19, the quantity demanded is 10 units. Based on this information, what is the marginal revenue resulting from an increase in output from 9 units to 10 units?

A. $10

B. $1

C. $19

D. $20

5. Because firms produce a differentiated product, each of the firms in a monopolistically competitive market faces a demand curve that is:

A. perfectly elastic.

B. downward sloping.

C. perfectly inelastic.

D. perfectly elastic or perfectly inelastic depending on whether the firm's output is a luxury or a necessity.

6. Suppose a monopolist is producing a level of output such that MR > MC. What should the firm do to maximize its profits?

A. The firm should increase output.

B. The firm should increase the price.

C. The firm should do nothing - it wants to maximize the difference between MR and MC in order to maximize its profits.

D. The firm should hire less labor.

7. Suppose the firms in a monopolistically competitive market are earning positive economic profits. What will happen to move the market to its long-run equilibrium?

A. The demand curves faced by firms in the market will shift to the right.

B. The firms' demand curves will become less elastic.

C. More close substitutes will appear in the market.

D. Some firms will exit the market if they can't cover all of their fixed and variable costs.

8. The Lerner Index is a measure of market power that focuses on:

A. the difference between a firm's product price and its marginal costs of production.

B. the share of the market controlled by the X largest firms in the market.

C. the ratio of the price of a firm's product to the price elasticity of demand for the product.

D. the sum of the squares of the market share of each firm in an industry.

9. The measure of market power that focuses on the share of the market controlled by the X largest firms in the market is known as:

A. the Lerner Index.

B. the Herfindahl-Hirschman Index.

C. the Minimum-Efficient Scale Index.

D. a concentration ratio.

10. The monopoly characteristic of monopolistically competitive firms ensures that such firms will earn positive economic profits over the long-run.

a. True

b. False

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