Question 4 Brenda, the consumer in Problem 3, now has to decide how many bagels

Question

Question 4

Brenda, the consumer in Problem 3, now has to decide how many bagels and how much coffee to have for breakfast. She has $8 of income to spend on bagels and coffee. Use the information given in the table in Problem 3 to answer the following questions.

a. Bagels cost $2 each, and coffee costs $2 per cup. Which bundles are on Brenda’s budget line? For each of these bundles, calculate the level of utility (in utils) that Brenda enjoys. Which bundle is her optimal bundle?

b. The price of bagels increases to $4, but the price of coffee remains at $2 per cup. Which bundles are now on Brenda’s budget line? For each bundle, calculate Brenda’s level of utility (in utils). Which bundle is her optimal bundle?

c. What do your answers to parts a and b imply about the slope of Brenda’s demand curve for bagels? Describe the substitution effect and the income effect of this increase in the price of bagels, assuming that bagels are a normal good.

Question 3 answers

Question 3

Consumption Bundle Quantity of bagels Quantity of coffee (cups) Total utility 0 0 0 0 2 28 0 4 40 1 2 48 1 3 54 2 0 28 2 2 56 3 1 54 3 2 62 4 0 40 4 2 66 d)keeping the quantity of coffee cups:1COstad) consta Total mU ageshuhyCbagels) 2 8 118 S6 20 2 3 62 6 Ll

Explanation / Answer

4) We are given the income of Brenda and the utilities at certain level of quantities of the goods consumed.

a) The prices of bagel and coffee are $2 each .

For finding the optimal quantity of good consumed we need to compute a budget line of Brenda

which is 2x+2y=8

she cannot spent more than 48 on both of them . So this is her constraint and we are given the prices

When she consumes only coffee , no bagel then x=0 and y= 4

no coffee and all bagel x= 4, y=0

2 units of each (2,2)

one unit of bagel and 3 of coffee and vice versa = (1,3) and (3,1)

So the bundles that lie on her budget line or in other words satisfy the equation above are (4,0),(3,1)(2,2),(1,3),(1,4)
Looking at table 3 with all these bundles we get the following values of utilities for each bundle

(4,0)= 40

(3,1)= 54

(2,2)= 56

(1,3)= 54

(0,4)= 40

The maximum utilty Brenda will get is at bundle (2,2) ie 56. so her optimla bundle is (2,2)

b) If price of bagel increases by $2 ie is now $4 and that of coffee remains the same .

the new budget line will be

4x+2y= 8

At 0 level of bagel and all coffee (0,4)

At all bagel and 0 coffee (2,0)

At one unit of bagel and 2 units of coffee (1,2)

Note that all these bundles will satisfy the equation of the new budget line .

The level of utility for each bundle is given below

(0,4)= 40

(2,0)= 28

(1,2)= 48

so maximum utility is for bundle (1,2) = 48 utils . Hence the optimal bundle will be (1,2)

c) From part a and b , we observe that as the price of bagel incraeses the quantity demanded by Brenda of it reduces ie the price and quantity are inversely related . So we have a downward sloping demand curve and a negative slope of demand curve for bagel .

When we say that bagel is a normal good it implies that with increase in the income of Brenda the demand for bagels will increase.

The increase in price of bagel will reduce the real purchasing power of it so Brenda purchases less of the good . in other words her same income the number of bagels purchased will reduce . This is known as the income effect ie less the income or real purchasing power less will be the units purchased.

Also there will be a secxond effect .With increase in price of bagels, it becomes less appealing or more expensive so Brenda would tend to reduce its consumption by a cheaper commodity , in this case is coffee . So she is substituting the expensive good by a cheaper one . this effect is known as the substitution effect.

Both of them would will reduce the quantity consumed of bagel .

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