Microeconomics Answers

Let 𝑓(𝑥1, 𝑥2) be a homothetic function. Show that its technical rate of substitution at (𝑥1, 𝑥2) equals its technical rate of substitution at (𝑡𝑥1,𝑡x2). Plot an isoquant map that displays this characteristic and provide some economic intuition for the meaning of this property.

Economists believe that production possibilities frontiers are often bowed because

What is the equation for demand?

(b) Suppose that instead of imposing the per-unit sales tax, the government sets a price ceiling of $7. Identify the quantity of soft drinks that will be exchanged in the market as a result of the price ceiling. Explain.

Competitive market Discussion: In your responses, comment on at least two posts from your peers and share an example of a company that experienced a change in revenue as the result of a change in the price of the good or service they provided. After reading your peers’ posts, explain which determinants of price elasticity of demand could be the cause of the change in demand.

Assume the demand for coffee increases and the supply of coffee decreases. Which of the following outcomes is certain to occur?

The equilibrium quantity of coffee will rise.

The equilibrium quantity of coffee will fall.

The equilibrium price of coffee will rise.

The equilibrium price of coffee will fall.

1.      Xan is a rational consumer who has an income of $11. He wishes to purchase both goods X and Y. Both goods are sold for $1.

(a)   Show that the condition for constrained utility maximization is satisfied. 

(b)  How much of good X and Y the individual should purchase to maximize utility if he spends all of his income.

(c)   Assuming that the individual has only the $11 to spend, determine the total utility the individual receives when he maximizes utility.

Units MUx MUy

1 15 12

2 11 9

3 9 6

4 6 5

5 4 3

6 3 2

7 1 1

1. The monopolist’s demand is represented by p=20-q, and the marginal cost function is MC(q)=2q, in which q is the quantity produced/sold. What is the production quantity and the price which can maximize the monopolist’s profit?

2. Show in a figure the profit and deadweight loss for a monopolistic firm.

3. The demand curve is p=10-q. The supply curve is p=2+q. Calculate the social welfare (consumer surplus + producer surplus) for the market equilibrium. If the government impose a price cap of 5, then how much is the deadweight loss? You may draw figures to assist your calculation.

4. For a monopolistic firm, the marginal cost is 20. The demand elasticity is -2. What is the optimal price for the firm to set?

5. Two identical firms(firm 1 and firm 2) face the following market demand curve p=40-(q1+q2), in which q1 and q2 are the production quantity of firm 1 and firm 2. Their marginal cost is a constant 4 per unit of product. What is the equilibrium price and quantity in the Cournot competition?

Let Y be a production set. We say that the technology is

additive if y in Y and y

in Y implies y + y

in Y . We say that the technology

is divisible if y in Y and 0< t<  1 implies that ty is in Y . Show that if a

technology is both additive and divisible, then Y must be convex and exhibit

constant returns to scale.

Consider a situation in which yields of tomatoes in a given year is destroyed by some pist attack on crops due to which price of tomatoes being effected. Explain how GDP deflator and cpi account for the price of tomatoes.