ECN100 HW2 3

Topics: Consumer theory, Supply and demand, Indifference curve Pages: 26 (6656 words) Published: January 12, 2015
HW 1

(1) Draw an indifference curve map with the quantity of pennies are on the horizontal axis and the quantity of nickels are on the vertical axis. Given the shape of your indifference curve, how would you describe the typical relationship between these two “products”?

The two goods are perfect substitutes for each other. 5pennies are equivalent to a nickel.

(2) You and I are in consumer equilibrium. CDs cost 10 dollars each and cassette tapes only 2 dollars each. I consume CDs and cassettes. You consume only cassettes. What can you infer about my MRS (marginal rate of substitution) of CDs and tapes? What about your MRS.

Since both individuals are in consumer equilibrium, for you, the MRS should equal the price ratio since you consume both goods. Hence MRS = 10/2 = 5.
For me since I consume only cassettes at my equilibrium, it implies that I consider CD’s a neutral good. Therefore my indifference curves are horizontal (assuming CD’s are on the horizontal axis). Hence MRS is zero, since no amount of increase in CD’s can change your utility unless you have more cassettes.

(3) The price of driving a car is 30 cents per mile. The cost of riding the bus is 60 cents per mile. At the moment, your Marginal Utility of the last mile of car transportation is 80 units, and the Marginal Utility of your last mile of bus transportation is 150 units. Are you maximizing your utility? Explain your answer.

If I’m maximizing my utility then the marginal utility derived from the last cent spent on each good must be equal.

The marginal utility from the last cent spent on driving a car is = 80/30 =8/3=2.67 The marginal utility from the last cent spent on riding the bus = 150/60 =5/2=2.5 Hence I’m not maximizing my utility. I can increase my utility by spending less on bus rides and more on driving the car.

(4) Let’s say your consumption basket is made up of two goods, “X” and “Y”. Your income is “I”. The market prices you face for these two goods are PX and PY. Draw an initial equilibrium point for your consumption of these two goods. (Restate the formula for the relation between your marginal rate of substitution and the market values of “X” and “Y” at the point of equilibrium.) Now, you suddenly crave good “X” much more relative to “Y” than previously. this do to your indifference curve and equilibrium position? Why? After you crave more “X” relative to “Y”, the price of “X” rises dramatically. your graph what does this do you your equilibrium position?

Now, your income doubles.

What does
Draw on

Graph your new equilibrium position.

By doing this exercise, you get a sense of how your real income and purchasing power, and consumption changes, as your tastes, income and market conditions change. Remember there are three components here:

Your psychological makeup – your indifference curve
Your income – the result of all your hard work and application of skills The prices you face, determined by the market.
In the “real world” this is a situation that will always hold true for you as you interact with the world of goods and services.
At the equilibrium, the MRS=price ratio = PX/PY. At the equilibrium, the indifference curve is tangential to the budget line.
MRS =MUX/MUY =PX/PY,
i.e. MUX/PX = MUY/PY
Now it is given that X is “craved” much more for relative to Y. Hence the indifference curves becomes steeper. That is now you are willing to give up more amount of Y to have a unit more of X. Alternatively, it can be said that you need more of Y to leave you indifferent for the same decrease in X.

Hence the slope of the indifference curve, i.e. the marginal rate of substitution increases, i.e. MUx/MUY increases.
We know that the price ratio doesn’t vary.
Hence at the original equilibrium, we have MUX/PX>MUY/PY.

Therefore you will consume more of X and less of Y at the new equilibrium, since your receiving more from the last dollar spent on X than Y.

Now the price of X rises. Since we are at an...
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