Question

1. Using a graphical representation and analytical explanation developed by you, generate a budgetary constraint model that shows the movement on the curve for different situations (income exceeds cost of items, income doesn't exceed cost of items etc). In addition, link the model developed back to its impact on choice and preferences.

2. Using a graphical representation and analytical explanation developed by you using a real world example as your point of reference, describe the theory of ordinal utility and consumer choice.

Answer 1

1.

To expain how an individual would decide his level of consumption we will make the following assumptions

1. An individual​ buys only two goods x and y.

2. His income is fixed here, $200

3 Price of good x is Px= $5, price of good y is Py= $10.

4.Utility function is defined as U(x,y)= x^1/2y^1/2

Now, we will solve for optimum demand for good x and y.

U(x,y) = √xy

Budget constraint = x.px+y.py=I

Px = $5, Py = $10, I = 200

MUx= du/dx = 1/2(y/x)^1/2

MUy= du/dy = 1/2(x/y)^1/2

At MUx/MUy=px/py we get optimum level of consumption

1/2(y/x)^1/2/1/2(x/y)^1/2= 5/10

y/x = 1/2

2y = x

We will put this value of x in the budget constraint

(2y).5+y.10 = 200

20y = 200

y = 10

x = 20

Thus, we got the optimum consumption of x and y with a constrained jncome of $200.

At point A in the diagram when income doesn't exceed cost of item we are at the budget line of our consumer. Now, if he wants to consume more say at point B where consumption of good x is 30 and that of good y is 15

30×5 + 15×10 = 300

He requires $300 to consume this much amount of good x and y which he can clearly not afford with his income of $200. Therefore , the point is outside of his budget line and also an unattainable combination of these goods. Any point on the budget line and below it is attainable point but at point A consumer is at his optimum level of consumption and would not choose any other point of the budget line.

2.

Theory of ordinary utility dates that consumer always prefers more but the utility he gets with each additional item consumed goes on decreasing.

Our everyday life situations provide us with ample examples say for example Casey decided to take part in a marathon and after finishing it she feels really hungry. So, she decides to order a pizza and after consumption of first pizza she still feels but she felt huge satisfaction from consuming that first pizza now, she decides to order one more pizza she is still hungry but her satisfaction from consumption of second pizza is less than that of first pizza so , she decides to order third pizza and now she is no more hungry and might throw up if she is asked to consume one more pizza.

From this example what we are trying to explain is that with each additional consumption her satisfaction kept on declining which is called as the diminishing rate of marginal returns.

Now, to explain how a consumer would decide her level of consumption based on her utility levels is by asking how much utility consumer would give at different levels of consumption and then compare it with price of the product. A consumer will stop consuming when the price is more than the utility derived from consumption.

We will make following hypothetical table amd diagram to explain it further

Number of consumption	Total Utility	Marginal Utility	Price
1	100	-	$10
2	138	38	$10
3	163	25	$10
4	177	14	$10
5	177	0	$10
6	164	-13	$10

Total Utility keeps on increasing up to a point after which it starts to decline. Marginal Utility declines with each additional level of consumption . Here till marginal utility is equal to or greater than the price consumer would buy the product. Which is at consumption level of 4 after which marginal utility is less than the price . Consumer would stop gaining any additional utility out of it and therefore will stop consuming.

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