Microeconomics Homework Help

3. (10 points) Suppose we have an agrarian economy that can utilize all its resources to produce either computer chips or wheat. Below is a table of possible combinations of both goods that can be produced if they are using their resources efficiently.

Assume that a monopolistically competitive industry is in the long-run equilibrium. Show the effect of a fall in demand on a firm’s price and profit in (a) the short run and in (b) the long run

(a) Explain verbally and digramatically why Christmas trees are cheaply sold on Christmas Eve (compared to their intial price) by considering both demand and supply. (b) Assuming zero disposal costs, why is the correct profit maximising price to charge for the unsold trees on Christmas Eve the one at which the elasticity of demand is equal to -1? Illustrate using a diagram. Would the price be lower still if there were some disposal costs that the seller would face to dispose of the unsold trees?

The government considers a Help for Houshold scheme to provide help for the rising energy costs facing households. Two programmes are considered: (i) paying a fixed amount in £ to a typical household or (ii) subsidising the price of energy by reducing the price of energy from p to (1- t)p, for t positive and less than 1. Provide economic arguments against and in favour of each of the programmes. Illustrate the economic effect of each of the programmes in a separate graph where energy is on the horizontal axis and all other goods are on the vertical axis. Illustrate the income and substitution effect of each programme in this graph assuming that both goods are normal goods. If your goal is economic efficiency, which programme do you favour? Explain and justify your answer.

The price of good x, px , is £1 and the price of y, py , is £1 and the budget is £100. The utility function for the two goods has strictly decreasing marginal rate of substitution. (a) Explain the meaning of strictly decreasing marginal rate of substitution in economic terms. Explain the opportunity cost of good x in economic terms. Calculate the opportunity cost of good x. (b) Use a graph where good x is on the horizontal axis and good y is on the vertical axis and draw the optimal solution to the utility maximisation problem subject to the budget constraint. Show the indifference curve that provides the optimal solution. What condition must be satisfied in this optimum? Interpret this condition economically in two different ways. Explain and sketch what could happen if the marginal rates of substitution are not strictly decreasing. Interpret.

CASE STUDY 1 Poverty Forces Two out of Nine Children to Quit School The hardship of a family in Pahang forces two out of nine children of a rubber to quit school, and the other four will have the same fate if the situation becomes worse. The head of the poor family said that he couldn't afford to send six children to school. He then decided to pull out two of them from school after failing to get help in order to provide enough food for everybody in the family. This is considered a sacrifice by the family in order to let the other four children continue their education. However, if the situation gets worse and without the help of anyone, there is a possibility that the four children will have to quit school as well. This sad story has gained the attention of the Ministry of Education which has contributed school uniforms and text books to them. The government has also decided to give the four children scholarships, and a monthly allowance of RM300 will soon be given to the family. 1. Define Scarcity, choice and opportunity cost. 2. Based on the above article, identify the problem of scarcity faced by this family, the choice that they had and the opportunity cost incurred from the decision made. 3. The allowance, the books and the school uniforms could certainly help alleviate the problem faced by this family. Does it mean the scarcity does not exist anymore? Why? 4. You win a free gift in a competition. Is the gift free? Explain.

2. In this exercise, we'll practice how to derive individual and market demand curves from utility functions and consumers' preferences: Assume that consumers in an economy can be divided into two groups: high-income consumers and low-income consumers. These consumers only consume two goods: x and y. The utility functions of the high-income and low- income groups are given as follows, respectively: a. Derive the demand function of good x for high-income consumers (Hint: Find the optimal xH function in terms of other constants like Px, Py, and I). b. Perform the natural log monotonic transformation on the utility function for low-income consumers to make this problem simpler (Hint: Take the natural log function of U (x, y), and apply the natural log properties on the exponents of the function). c. Derive the demand function of good x for low-income consumers (Hint: Use the function in part (b) to find the optimal x,function in terms of other constants like Px, Py, and I₁. Using the function in (b) is just easier, but you are not obligated to use it). Now assume in the remaining parts that the monthly income of low-income consumers is $300, and the monthly income of high-income consumers is $6000. d. Write down the demand functions of good x for low-income consumers and high-income consumers at the given incomes. e. At what range of prices do high-income consumers stop buying product x? At what range of prices do low- income consumers stop buying product x? f. Write down the market demand equation for good x. g. At what price would you expect to see a kink in the market demand curve for good x? Explain your answer.

4. The following incomplete table shows a firm's various costs of producing up to 3 units of output. Fill in the table's empty boxes and show how you got your solutions.

a. If there were many suppliers of diamonds, what would be the price and quantity? b. If there were only one supplier of diamonds, what would be the price and quantity? c. If Russia and South Africa formed a cartel, what would be the price and quantity? If the countries split the market evenly, what would be South Africa's production and profit? What would happen to South Africa's profit if it increased its production by while Russia stuck to the cartel agreement? d. Use your answers to part (c) to explain why cartel agreements are often not successful.

Consider the optimization problem: Question 3 f(x, y) = 20 - 2x + 3xy s. t. 4x + 2y = 100