Microeconomics Answers

you were planning to spend saturday working at your part-time job but a friend asks you to go skiing

A person’s utility function is of the form U(x,y) = 5xy. The prices of good x and y are Px = $4 and Py = $2, respectively. The person’s income is $1200.

(a) Show that these preferences are homothetic?

(b) What quantities of x and y should the consumer purchase to maximize his

utility?

(c) Determine the person’s income offer curve (IOC). Draw it.

(d) Explain whether each of the two goods is normal or inferior.

(e) Derive the Engel curve for x. Draw it.

D. Complete the following table and graph the utility curves for Kali and describe the

slope of her utility curves in the context of her consumption for mangoes. (12 marks)

Eggplants Total Utility Marginal Utility

(TU) (MU)

1 105

2 195

4 300

6 30

8 375

9 4

Household Consumption and Budget Constraints

Kali lives on mangoes and avocados, Pm = $5, Pa = $10, and her income is $200.

A. Identify her budget constraint equation and illustrate Kali’s budget line on a graph

with eggplants on the horizontal axis and soursop on the vertical axis.

B. Identify and illustrate on a new graph Kali’s new budget constraint if her income

doubled, the price of eggplants doubled, and the price of soursop remained constant.

Stuart's utility function for goods X and Y is represented as U(X,Y)=X0.8Y0.2. Assume that his income is $100 and the prices of goods X and Y are $20 and $10, respectively.

(a) Express his marginal rate of substitution (MRS) between goods X and Y. As the amount of X increases relative to the amount of Y along the same indifference curve, does the MRS increase or decrease? Explain.

(b) What is his optimal consumption bundle (X*, Y*), given income and prices of the two goods?

(c) How will this bundle change when all prices double and income is held constant? When all prices double AND income doubles?

(d) Derive the demand curve for good X and demand curve for good Y.

Do each of a-d, both geometrically (you need not be precise) and using calculus. There are only two goods; x is the quantity of one good and y of the other. Your income is I and u(x,y) = xy + x + y.

(a) Px = $2; Py = $1; I = $15. Suppose Py rises to $2. By how much must I increase in order that you be as well off as before?

(b) In the case described in part (a), assuming that I does not change, what quantities of each good are consumed before and after the price change? How much of each change is a substitution effect? How much is an income effect?

(c) Px = $2; I =$15. Graph the amount of Y you consume as a function of Py , for values of Py ranging from $0 to $10 (your ordinary demand curve for Y).

(d) With both prices equal to $1, show how consumption of each good varies as I changes from $0 to $100.

Kali lives on mangoes and avocados, Pm = $5, Pa = $10, and her income is $200.

A. Identify her budget constraint equation and illustrate Kali’s budget line on a graph

with eggplants on the horizontal axis and soursop on the vertical axis.

B. Identify and illustrate on a new graph Kali’s new budget constraint if her income

doubled, the price of eggplants doubled, and the price of soursop remained constant.

C. Explain the impact on her real income when the price changed in the scenario in B

assuming income had remained constant.

D. Complete the following table and graph the utility curves for Kali and describe the

slope of her utility curves in the context of her consumption for mangoes.

Kali lives on mangoes and avocados, Pm = $5, Pa = $10, and her income is $200.Identify her budget constraint equation and illustrate Kali’s budget line on a graph

with eggplants on the horizontal axis and soursop on the vertical axis.

In early 2015 the price of condominium in Singapore rose. In a demand and supply model,

shifts in what curve or curves could have brought about the higher price?

Variant 5.

A worker gets wages (salary) from a capitalist. What function will money play in this case? What functions of money do you know? (5 points).

 The productivity of labour has increased twice. What will happen with the volume of output, value of one commodity, the value of total output? What is the difference between labour productivity and labour intensity? (5 points).

The price of commodity has increased from 0,5 to 1 dol. and volume of demand has decreased from 10 to 5 units. Determine the coefficient of price elasticity and comment the result. (10 points).