Calculate the income elasticity of demand etai are

Question

1. PERFECT COMPETITION

GREYROCK INC. produces light bulbs and is a member of a perfectly competitive market. The exact demand curve is not known. However, you observed that Q₁ = 200 light bulbs are sold at a price of P₁ = 900 in the entire industry. At a price of P₂ = 400 consumers purchase 600 units of the good (Q₁ = 600). The whole industry is composed of N = 10 firms. The total cost function of each company reads TC(Q) = 50Q + 100.

a) Construct the market demand curve.

b) Calculate the profit maximizing output as well as the corresponding price and economic profit.

c) Calculate the average costs at this level of output.

d) Is the market in equilibrium? Why or why not?

2. MONOPOLY

You are hired to consult the ADOL CORPORATION, the single supplier of a special medical care product that promises to mitigate headache. The company sells a quantity of Q = 1 Mio at a price of P = $100. The marginal costs are MC = $40 and the average costs at this level of output are AC 1,000,000 = $90. You know that price elasticity of demand η_D = -2.

a) Would you recommend the company to change its pricing behavior?

b) What's the marginal revenue of the firm if it maximizes profits?

c) The managers of ADOL believe that investing $100,000 in advertising will increase total sales by $300,000. Is this the optimal amount to spend on advertising? If not, should the company spend less or more?

d) What are the characteristics of monopolies and why is the output inefficient? Under which circumstances are they likely to occur?

3. MONOPOLY II 

Suppose that the government is the only provider of water. The market demand function reads D: Q(P) = 50 - 2P. The government's total cost for producing water are described as follows: TC(Q) = 100 + 10Q.

a) What price will the government charge if it wants to ensure an efficient allocation of water?

b) What price will the government charge if it wants to maximize profits?

c) Calculate the economic profit in both scenarios.

d) Calculate the dead weight loss (loss in welfare) resulting from the inefficient allocation in example b)

e) How will the consumer as well as the producer surplus change and why?

4. PRICE DISCRIMINATION 

The XOCOLAT FACTORY operates in two different and wholly independent markets. It sells a special kind of peanut butter cups in both, the US and in Europe. The demand curve for the market in the US is described as P_US = 320 - 8Q_US" and the demand function for the European market is P_EU = 160 - 2Q_EU". The marginal cost function reads MC = 5 + 2Q where Q = Q_US + Q_EU. There are fixed costs of FC = $1,000.

a) How many units of output should the XOCOLAT FACTORY sell in the European market?

b) What is the XOCOLAT FACTORY's optimal level of output in the United States?

c) Calculate the optimal prices in each market.

d) What would be the profit of the XOCOLAT FACTORY if it decided to engage in price discrimination?

5. REGRESSION ANALYSIS 

Using regression analysis, the GREENHOUSE COMPANY obtained the following estimate of the demand function for vegetables. The t-values are given in the parentheses below coefficients. (R² = 0.82)

Q_G = 500 - 6.8P_G + 4.2P_R + 1.2A_G - 0.0012A²_G + 0.21I + ∈
         (3.2)    (7.5)     (12.4)    (9.2)        (6.8)             (1.1)

Q_G is the quantity of vegetables demanded, P_G is the price the Greenhouse company charges (in dollars), P_R is the price of its main competitor (in dollars), A_G are advertising expenditures (in dollars) and I is disposable income per capita (in 100 dollars).

a) The company wants to increase its output by 100 units. Think of a realistic scenario how it might be able to achieve this goal? Provide a reasonable suggestion regarding potential investments the company ought to commit.

b) The company decides to reduce its price by $5. What is, ceteris paribus, the estimated effect of such a price reduction?

c) If the competitor decides to raise its prices by $10, how would the GREENHOUSE COMPANY'S Output change?

d) Is it reasonable for the GREENHOUSE COMPANY to increase its output by spending $1,000 on advertising?

e) Interpret the R1 and the t-values, what do they suggest in this specific case? What is the error term ???

6. ELASTICITIES 

Now assume that the price of the GREENHOUSE COMPANY is P₁ = $80, the price of its main competitor is P₁ = $100 and that GREENHOUSE spends A₁ = $300 on advertising. The income is I = $120,000. Note that I is measured in $100. You are asked to interpret the results of your calculations properly.
a) Calculate the own-price elasticity of demand η_PG".

b) Can you determine whether the products are complementary or substitutive goods without calculating the exact result? Why or why not? Calculate the cross price elasticity of demand, η_PR". Are the goods complementary or substitutive goods?

c) Calculate the income elasticity of demand η_I. Are vegetables inferior goods?